~Y1V~~F~cd5 ~ +-UL can~~o-n (a)oJ) ~~
A4 Q n~ c ~ Q Wnd b
~
~ that
f (c) = b ~ a ~+(x)ciJshya
The AvM1LfF V~ 1) Q FLvYL~middot
i + M eoYl~~ GYL [a 6J) ~ t-fu oVLLQ~ V~ 1J OYL +Iu ~va) ~
f-iCO= (+CxJdr = +CC-)b-CL J
0
~~~ -f(k)~(X-tIY) [Ojd1 ~
A(t)~ ~~o )(x-~+dx+)cLf ()
= hl 1-3+ xj+)f= ~( ~ + Ii-r~
c
To ~ Q +Ccj = ~ = c~+ d c + 1
C -+ ~ c - lQ == 0 -732-2-+ Co e - I 0 = 05
= -[PplusmnJ3to+lJO = -I + Jf3qC - to 0
~ = - + i 3C1 ~~ ~
o lt - --- 3cC lt ~ 3
30
__-- Condi-t-zG-n F ~oY1-J-inu()u-s oYeA- Ca 0]__ ______ And f~ (X+-l)2 _is Can-hnU-ChA-S oVershy
______~[0) i] ai heL -+ i S Q trCAolgto 0 middot ___
___---++-EorI f(xl = ex -t-11L) Co)] 1 +-O+a-Q Qle~ R~ under cuCV e is ( z _ ~N
__ _ J ex ~ 2x-+ JuLi ~r o
____--Ibe over~e avvu 0-~ WIcl+h
____ G ~ j 5 ~(p ~ ~ ampL lt = 13o 3-middot ~ 3
- - h- e- a- r o at rec(-~ te Z X ~ ~-p - -CWmiddot-J 3
otfjyGEbull
Matb 112 REFERENCE SHEET
U1+1
1 furdU- -+C k+1
f du 1 u
3 fedu- eN + C 5 2 - -Arctan-+C4 fJ tu 2 - Ansinf + C +u a aa -u a
6 f sinu du - -cosu+ C 7 foosu du-sinu+C
10 leCutanUdu -secu + C 11 fcscucotu du - -escu + C
12 ftanudu - -lnlcosul+C 13 f cotudu-Inlsinu 1+ C
14 fsccudU -Insccu+tanu+ C 15- f escu du -Incscu- cot~ + C
IrigogometJ1s Identities aDd Triangles
8 xS1D shy1 sin2 u + 008
2 u - 1 a
2 22 1+ tan U - sec u
2 23 1+ cot u esc u x
tan8-shyx a
4 sin2u - 2sin ucosu II
COS 2 U -sin2 u x
sect) - shy5 cos2u - 200s2u-1 a
1- 2sin 2 u
1efeKelaquoCe
ExOYYl~s) u- sJ-s-ft-fuhcra I sheetmiddotmiddot
0(~-x l
)sin s X 4 ~~
ft de Cosx = ~CcI x-ctJcx I = C5CaX~CO+~ ~x sin Xbull Sil1fx
( I rI ~---o~-d- ~J plusmn= e2)( --------------
( ~ =1 =J~(l+-~) ctu-- I raquo~
----~--~~-~~~--------~ ~~~~--------~~~cLu-- --L~
( ~u- --- L
2 Jrr~ ~~ -~------
+ ~
( -
- 1- c4 shy-------J- X~~)+5 ~-----------shy
pound
---------s4 1x +i)~--shy---------==============----j i +-u t
th~ Pr-oblevYS - tJU)
q) S~loX ~2-x~ tX-a 5In(LXJ+c
f-evieuJ
ampoJ~
CD S--J 3~X~~X4 jXl_)~ 11 dj
amp~
~) 5e2~~X~ctt
ShaLU ~oJ- fh e rYJ ecv-n Value Jh ~ frrr~cr~+o ~= Lf~) ~ [13]
I - cO5 (dLc) bull 2
SYlU= 2
r[LSe i JeNt-n esJ 1 +- Co s C~u-)L - cos
l U- =
S(I - eO(~X))(l t-~~S(~XJ) rhf
~ ~ (I - Cns2(2)lt))ctx -= ~ ~ - ~reoS(2X)dX-
- ~ ~ I + ~SC4X)~ -= - ~ 51+ ~os (4x~dx
- ~ x - 1 q S i r (tix) -t- Cshy~ 8 ~==============--____middot 6-x=~ Sh(L~) +9
( ~ k~s n lA + C ~ 4rc s ex +-~) + j~4-~~ ~ ~
copy ~ -co--n 2
6 c4 lA-~~ ~ 00vc=-d~ -7gt ~du=ampci+
~~-cnY4lA ~
d S~cu- -)amplA = d-tCAnA -dLA--4~-JX -z~~
6) == est LAshy
oLuJ = - CJ~2u-cLushy- ohu ==- C-Ll c-2u ~
-------
(sect) CD-r+ I -x - SLL V~ -) - 2 u~ + ~ ~ 3
~lt 3~0- 3 (-1) ~
SsinlXrI = (6QDs2x)~ [ide-nJ-tfies] Cos 2 x J-If- j cos2)lt ~
51-)cosltx +~osYx J =-~ - d~ + cospclo shy~os 2x middot vvy- JkoSx ~ CD~ xp
2)~C-21-- - ~ -+ eampltl x)dx = -tQn~ -2 ~ + SCDsxdx ~ I + ~05(~x)~ = amp X -+-j~S n (ax) -l- ~
-
(bYl X - ~ A+~ SihClxi + ~~ ( x d _ S x dshy
J X2ltX-t-d X -I-(X~d-+I)-
S1+~X-J)2dJ+ - )lt =- LA-+- ILt= f-
( LA- + I cik clv = dJ- [so l v e ~ 1-] ) l +uL
~ LA- ~ ~ LA --- Q
Second C0~ +U- ~ w LA--s LA-r c1LuJ ==- ~Aclu ~~ lw 1+ C plusmnoluJ= ~
shy
egtL_
~(x-) +--h~ + lX-IY +b
0-T f1~ vvo -r -c01 f == (YrJJC0 S J -+ = rygt1 -XOr-) - --rtpYl~I1--OfSI(flSOf) l~ --I- ~
(4)~vj+h -yrp~-y)dS)Y1Uur5=~Y1poundXDrS) (~)wrr-~ u-+ (+)h~q~ - ~~~
-pY1C~ -=--nyJ l) + hY) -9- - -= -rrp l1S shyi Y1 U--O~ Yl pound
7py-rv+5-t--yTYlTo) d S Y)oeLX~f5--=-~ shy_ 0 -Y) C0 db) -YVOi-5 fCjVlS
- YJ Qr1-f] -trp-c-4- _YrfJ - _ ~ II s U)q- ( shy-frp ~ - = P-c_X-~ -yrp )
X X -I] ~ tX 1- =- shyT I tJ Gf)sVor ) (iJd)
[~Jvw ~I = 0
YJh -= 11 Q
(~d f~~j-dPJ 11 1k L ~jJ JI I
hi+ t _ --yyp -e 0 CO) ~~ 7vp )( - T 1 == ( I )v---op~~~X+_I jJ IV X G =P )( + I ()
tj x~P-o ~Y1 ~ xvvap~)(~)
-U---+-(-h-t-X-)8--~-h-+-X-)--+=-lt---)-+ LY] 8 - YI 71Z -elf- Z T tIE
---nrp7r_TJh-rYJ)f - -vrplW~ ~~f -np h= Sf
fvp x -== YY(J ~
[1X -OJ- )1 lOS] 1vpxe -= -yyp - L-I1= X~ H+X==Y1
l -z z 7rp h+~Xf-5 pound
An5 lJ er-s -Iv ffuJ 0J~
=_~ =~(j)_ f X dJtshyj ~8-x2-ax
~CJlve
_---~ == ~LLf-j (~Ji) =- 0id-fj - ~JX---- - ctf J~ff j2 ~--
~l~~ - ~~-~---------
o
S-2 ciu ==- 5U--~~ ~--
- U-- + c - I ~=e - d-
LA- == -tarv- (sx) cLu- = 5 ~poundL1-(S X) dJshy
~=-~c~xJ4
2 JtOYISx) --f-~ 5
= -e - +- C -7- - ~~
-I- ~
~f=-~ -=-0 ~ -se -~e~=-~
shy~z = ~ -O=~
- 2
- LAshy3
--2~ _ ~ gt 3
middot S hcnu ~ot-+4 Yf1ecv-n V~~ ~ ~ tl-o Lj = Lj(X~ I ) (V-eA- DJ J X L
CD C~I~ ~ [) 3 J 5 j LJL cROy-y~ 7 j 0 x -=FO Cpound-vLd j poundLJ ~ A~~c-P ~
GJA (Jl =- I ( 34 ex 2 + () ~ ==- ~ 3 -I J)(2 If 3
30
__-- Condi-t-zG-n F ~oY1-J-inu()u-s oYeA- Ca 0]__ ______ And f~ (X+-l)2 _is Can-hnU-ChA-S oVershy
______~[0) i] ai heL -+ i S Q trCAolgto 0 middot ___
___---++-EorI f(xl = ex -t-11L) Co)] 1 +-O+a-Q Qle~ R~ under cuCV e is ( z _ ~N
__ _ J ex ~ 2x-+ JuLi ~r o
____--Ibe over~e avvu 0-~ WIcl+h
____ G ~ j 5 ~(p ~ ~ ampL lt = 13o 3-middot ~ 3
- - h- e- a- r o at rec(-~ te Z X ~ ~-p - -CWmiddot-J 3
otfjyGEbull
Matb 112 REFERENCE SHEET
U1+1
1 furdU- -+C k+1
f du 1 u
3 fedu- eN + C 5 2 - -Arctan-+C4 fJ tu 2 - Ansinf + C +u a aa -u a
6 f sinu du - -cosu+ C 7 foosu du-sinu+C
10 leCutanUdu -secu + C 11 fcscucotu du - -escu + C
12 ftanudu - -lnlcosul+C 13 f cotudu-Inlsinu 1+ C
14 fsccudU -Insccu+tanu+ C 15- f escu du -Incscu- cot~ + C
IrigogometJ1s Identities aDd Triangles
8 xS1D shy1 sin2 u + 008
2 u - 1 a
2 22 1+ tan U - sec u
2 23 1+ cot u esc u x
tan8-shyx a
4 sin2u - 2sin ucosu II
COS 2 U -sin2 u x
sect) - shy5 cos2u - 200s2u-1 a
1- 2sin 2 u
1efeKelaquoCe
ExOYYl~s) u- sJ-s-ft-fuhcra I sheetmiddotmiddot
0(~-x l
)sin s X 4 ~~
ft de Cosx = ~CcI x-ctJcx I = C5CaX~CO+~ ~x sin Xbull Sil1fx
( I rI ~---o~-d- ~J plusmn= e2)( --------------
( ~ =1 =J~(l+-~) ctu-- I raquo~
----~--~~-~~~--------~ ~~~~--------~~~cLu-- --L~
( ~u- --- L
2 Jrr~ ~~ -~------
+ ~
( -
- 1- c4 shy-------J- X~~)+5 ~-----------shy
pound
---------s4 1x +i)~--shy---------==============----j i +-u t
th~ Pr-oblevYS - tJU)
q) S~loX ~2-x~ tX-a 5In(LXJ+c
f-evieuJ
ampoJ~
CD S--J 3~X~~X4 jXl_)~ 11 dj
amp~
~) 5e2~~X~ctt
ShaLU ~oJ- fh e rYJ ecv-n Value Jh ~ frrr~cr~+o ~= Lf~) ~ [13]
I - cO5 (dLc) bull 2
SYlU= 2
r[LSe i JeNt-n esJ 1 +- Co s C~u-)L - cos
l U- =
S(I - eO(~X))(l t-~~S(~XJ) rhf
~ ~ (I - Cns2(2)lt))ctx -= ~ ~ - ~reoS(2X)dX-
- ~ ~ I + ~SC4X)~ -= - ~ 51+ ~os (4x~dx
- ~ x - 1 q S i r (tix) -t- Cshy~ 8 ~==============--____middot 6-x=~ Sh(L~) +9
( ~ k~s n lA + C ~ 4rc s ex +-~) + j~4-~~ ~ ~
copy ~ -co--n 2
6 c4 lA-~~ ~ 00vc=-d~ -7gt ~du=ampci+
~~-cnY4lA ~
d S~cu- -)amplA = d-tCAnA -dLA--4~-JX -z~~
6) == est LAshy
oLuJ = - CJ~2u-cLushy- ohu ==- C-Ll c-2u ~
-------
(sect) CD-r+ I -x - SLL V~ -) - 2 u~ + ~ ~ 3
~lt 3~0- 3 (-1) ~
SsinlXrI = (6QDs2x)~ [ide-nJ-tfies] Cos 2 x J-If- j cos2)lt ~
51-)cosltx +~osYx J =-~ - d~ + cospclo shy~os 2x middot vvy- JkoSx ~ CD~ xp
2)~C-21-- - ~ -+ eampltl x)dx = -tQn~ -2 ~ + SCDsxdx ~ I + ~05(~x)~ = amp X -+-j~S n (ax) -l- ~
-
(bYl X - ~ A+~ SihClxi + ~~ ( x d _ S x dshy
J X2ltX-t-d X -I-(X~d-+I)-
S1+~X-J)2dJ+ - )lt =- LA-+- ILt= f-
( LA- + I cik clv = dJ- [so l v e ~ 1-] ) l +uL
~ LA- ~ ~ LA --- Q
Second C0~ +U- ~ w LA--s LA-r c1LuJ ==- ~Aclu ~~ lw 1+ C plusmnoluJ= ~
shy
egtL_
~(x-) +--h~ + lX-IY +b
0-T f1~ vvo -r -c01 f == (YrJJC0 S J -+ = rygt1 -XOr-) - --rtpYl~I1--OfSI(flSOf) l~ --I- ~
(4)~vj+h -yrp~-y)dS)Y1Uur5=~Y1poundXDrS) (~)wrr-~ u-+ (+)h~q~ - ~~~
-pY1C~ -=--nyJ l) + hY) -9- - -= -rrp l1S shyi Y1 U--O~ Yl pound
7py-rv+5-t--yTYlTo) d S Y)oeLX~f5--=-~ shy_ 0 -Y) C0 db) -YVOi-5 fCjVlS
- YJ Qr1-f] -trp-c-4- _YrfJ - _ ~ II s U)q- ( shy-frp ~ - = P-c_X-~ -yrp )
X X -I] ~ tX 1- =- shyT I tJ Gf)sVor ) (iJd)
[~Jvw ~I = 0
YJh -= 11 Q
(~d f~~j-dPJ 11 1k L ~jJ JI I
hi+ t _ --yyp -e 0 CO) ~~ 7vp )( - T 1 == ( I )v---op~~~X+_I jJ IV X G =P )( + I ()
tj x~P-o ~Y1 ~ xvvap~)(~)
-U---+-(-h-t-X-)8--~-h-+-X-)--+=-lt---)-+ LY] 8 - YI 71Z -elf- Z T tIE
---nrp7r_TJh-rYJ)f - -vrplW~ ~~f -np h= Sf
fvp x -== YY(J ~
[1X -OJ- )1 lOS] 1vpxe -= -yyp - L-I1= X~ H+X==Y1
l -z z 7rp h+~Xf-5 pound
An5 lJ er-s -Iv ffuJ 0J~
=_~ =~(j)_ f X dJtshyj ~8-x2-ax
~CJlve
_---~ == ~LLf-j (~Ji) =- 0id-fj - ~JX---- - ctf J~ff j2 ~--
~l~~ - ~~-~---------
o
S-2 ciu ==- 5U--~~ ~--
- U-- + c - I ~=e - d-
LA- == -tarv- (sx) cLu- = 5 ~poundL1-(S X) dJshy
~=-~c~xJ4
2 JtOYISx) --f-~ 5
= -e - +- C -7- - ~~
-I- ~
~f=-~ -=-0 ~ -se -~e~=-~
shy~z = ~ -O=~
- 2
- LAshy3
--2~ _ ~ gt 3
middot S hcnu ~ot-+4 Yf1ecv-n V~~ ~ ~ tl-o Lj = Lj(X~ I ) (V-eA- DJ J X L
CD C~I~ ~ [) 3 J 5 j LJL cROy-y~ 7 j 0 x -=FO Cpound-vLd j poundLJ ~ A~~c-P ~
GJA (Jl =- I ( 34 ex 2 + () ~ ==- ~ 3 -I J)(2 If 3
Matb 112 REFERENCE SHEET
U1+1
1 furdU- -+C k+1
f du 1 u
3 fedu- eN + C 5 2 - -Arctan-+C4 fJ tu 2 - Ansinf + C +u a aa -u a
6 f sinu du - -cosu+ C 7 foosu du-sinu+C
10 leCutanUdu -secu + C 11 fcscucotu du - -escu + C
12 ftanudu - -lnlcosul+C 13 f cotudu-Inlsinu 1+ C
14 fsccudU -Insccu+tanu+ C 15- f escu du -Incscu- cot~ + C
IrigogometJ1s Identities aDd Triangles
8 xS1D shy1 sin2 u + 008
2 u - 1 a
2 22 1+ tan U - sec u
2 23 1+ cot u esc u x
tan8-shyx a
4 sin2u - 2sin ucosu II
COS 2 U -sin2 u x
sect) - shy5 cos2u - 200s2u-1 a
1- 2sin 2 u
1efeKelaquoCe
ExOYYl~s) u- sJ-s-ft-fuhcra I sheetmiddotmiddot
0(~-x l
)sin s X 4 ~~
ft de Cosx = ~CcI x-ctJcx I = C5CaX~CO+~ ~x sin Xbull Sil1fx
( I rI ~---o~-d- ~J plusmn= e2)( --------------
( ~ =1 =J~(l+-~) ctu-- I raquo~
----~--~~-~~~--------~ ~~~~--------~~~cLu-- --L~
( ~u- --- L
2 Jrr~ ~~ -~------
+ ~
( -
- 1- c4 shy-------J- X~~)+5 ~-----------shy
pound
---------s4 1x +i)~--shy---------==============----j i +-u t
th~ Pr-oblevYS - tJU)
q) S~loX ~2-x~ tX-a 5In(LXJ+c
f-evieuJ
ampoJ~
CD S--J 3~X~~X4 jXl_)~ 11 dj
amp~
~) 5e2~~X~ctt
ShaLU ~oJ- fh e rYJ ecv-n Value Jh ~ frrr~cr~+o ~= Lf~) ~ [13]
I - cO5 (dLc) bull 2
SYlU= 2
r[LSe i JeNt-n esJ 1 +- Co s C~u-)L - cos
l U- =
S(I - eO(~X))(l t-~~S(~XJ) rhf
~ ~ (I - Cns2(2)lt))ctx -= ~ ~ - ~reoS(2X)dX-
- ~ ~ I + ~SC4X)~ -= - ~ 51+ ~os (4x~dx
- ~ x - 1 q S i r (tix) -t- Cshy~ 8 ~==============--____middot 6-x=~ Sh(L~) +9
( ~ k~s n lA + C ~ 4rc s ex +-~) + j~4-~~ ~ ~
copy ~ -co--n 2
6 c4 lA-~~ ~ 00vc=-d~ -7gt ~du=ampci+
~~-cnY4lA ~
d S~cu- -)amplA = d-tCAnA -dLA--4~-JX -z~~
6) == est LAshy
oLuJ = - CJ~2u-cLushy- ohu ==- C-Ll c-2u ~
-------
(sect) CD-r+ I -x - SLL V~ -) - 2 u~ + ~ ~ 3
~lt 3~0- 3 (-1) ~
SsinlXrI = (6QDs2x)~ [ide-nJ-tfies] Cos 2 x J-If- j cos2)lt ~
51-)cosltx +~osYx J =-~ - d~ + cospclo shy~os 2x middot vvy- JkoSx ~ CD~ xp
2)~C-21-- - ~ -+ eampltl x)dx = -tQn~ -2 ~ + SCDsxdx ~ I + ~05(~x)~ = amp X -+-j~S n (ax) -l- ~
-
(bYl X - ~ A+~ SihClxi + ~~ ( x d _ S x dshy
J X2ltX-t-d X -I-(X~d-+I)-
S1+~X-J)2dJ+ - )lt =- LA-+- ILt= f-
( LA- + I cik clv = dJ- [so l v e ~ 1-] ) l +uL
~ LA- ~ ~ LA --- Q
Second C0~ +U- ~ w LA--s LA-r c1LuJ ==- ~Aclu ~~ lw 1+ C plusmnoluJ= ~
shy
egtL_
~(x-) +--h~ + lX-IY +b
0-T f1~ vvo -r -c01 f == (YrJJC0 S J -+ = rygt1 -XOr-) - --rtpYl~I1--OfSI(flSOf) l~ --I- ~
(4)~vj+h -yrp~-y)dS)Y1Uur5=~Y1poundXDrS) (~)wrr-~ u-+ (+)h~q~ - ~~~
-pY1C~ -=--nyJ l) + hY) -9- - -= -rrp l1S shyi Y1 U--O~ Yl pound
7py-rv+5-t--yTYlTo) d S Y)oeLX~f5--=-~ shy_ 0 -Y) C0 db) -YVOi-5 fCjVlS
- YJ Qr1-f] -trp-c-4- _YrfJ - _ ~ II s U)q- ( shy-frp ~ - = P-c_X-~ -yrp )
X X -I] ~ tX 1- =- shyT I tJ Gf)sVor ) (iJd)
[~Jvw ~I = 0
YJh -= 11 Q
(~d f~~j-dPJ 11 1k L ~jJ JI I
hi+ t _ --yyp -e 0 CO) ~~ 7vp )( - T 1 == ( I )v---op~~~X+_I jJ IV X G =P )( + I ()
tj x~P-o ~Y1 ~ xvvap~)(~)
-U---+-(-h-t-X-)8--~-h-+-X-)--+=-lt---)-+ LY] 8 - YI 71Z -elf- Z T tIE
---nrp7r_TJh-rYJ)f - -vrplW~ ~~f -np h= Sf
fvp x -== YY(J ~
[1X -OJ- )1 lOS] 1vpxe -= -yyp - L-I1= X~ H+X==Y1
l -z z 7rp h+~Xf-5 pound
An5 lJ er-s -Iv ffuJ 0J~
=_~ =~(j)_ f X dJtshyj ~8-x2-ax
~CJlve
_---~ == ~LLf-j (~Ji) =- 0id-fj - ~JX---- - ctf J~ff j2 ~--
~l~~ - ~~-~---------
o
S-2 ciu ==- 5U--~~ ~--
- U-- + c - I ~=e - d-
LA- == -tarv- (sx) cLu- = 5 ~poundL1-(S X) dJshy
~=-~c~xJ4
2 JtOYISx) --f-~ 5
= -e - +- C -7- - ~~
-I- ~
~f=-~ -=-0 ~ -se -~e~=-~
shy~z = ~ -O=~
- 2
- LAshy3
--2~ _ ~ gt 3
middot S hcnu ~ot-+4 Yf1ecv-n V~~ ~ ~ tl-o Lj = Lj(X~ I ) (V-eA- DJ J X L
CD C~I~ ~ [) 3 J 5 j LJL cROy-y~ 7 j 0 x -=FO Cpound-vLd j poundLJ ~ A~~c-P ~
GJA (Jl =- I ( 34 ex 2 + () ~ ==- ~ 3 -I J)(2 If 3
1efeKelaquoCe
ExOYYl~s) u- sJ-s-ft-fuhcra I sheetmiddotmiddot
0(~-x l
)sin s X 4 ~~
ft de Cosx = ~CcI x-ctJcx I = C5CaX~CO+~ ~x sin Xbull Sil1fx
( I rI ~---o~-d- ~J plusmn= e2)( --------------
( ~ =1 =J~(l+-~) ctu-- I raquo~
----~--~~-~~~--------~ ~~~~--------~~~cLu-- --L~
( ~u- --- L
2 Jrr~ ~~ -~------
+ ~
( -
- 1- c4 shy-------J- X~~)+5 ~-----------shy
pound
---------s4 1x +i)~--shy---------==============----j i +-u t
th~ Pr-oblevYS - tJU)
q) S~loX ~2-x~ tX-a 5In(LXJ+c
f-evieuJ
ampoJ~
CD S--J 3~X~~X4 jXl_)~ 11 dj
amp~
~) 5e2~~X~ctt
ShaLU ~oJ- fh e rYJ ecv-n Value Jh ~ frrr~cr~+o ~= Lf~) ~ [13]
I - cO5 (dLc) bull 2
SYlU= 2
r[LSe i JeNt-n esJ 1 +- Co s C~u-)L - cos
l U- =
S(I - eO(~X))(l t-~~S(~XJ) rhf
~ ~ (I - Cns2(2)lt))ctx -= ~ ~ - ~reoS(2X)dX-
- ~ ~ I + ~SC4X)~ -= - ~ 51+ ~os (4x~dx
- ~ x - 1 q S i r (tix) -t- Cshy~ 8 ~==============--____middot 6-x=~ Sh(L~) +9
( ~ k~s n lA + C ~ 4rc s ex +-~) + j~4-~~ ~ ~
copy ~ -co--n 2
6 c4 lA-~~ ~ 00vc=-d~ -7gt ~du=ampci+
~~-cnY4lA ~
d S~cu- -)amplA = d-tCAnA -dLA--4~-JX -z~~
6) == est LAshy
oLuJ = - CJ~2u-cLushy- ohu ==- C-Ll c-2u ~
-------
(sect) CD-r+ I -x - SLL V~ -) - 2 u~ + ~ ~ 3
~lt 3~0- 3 (-1) ~
SsinlXrI = (6QDs2x)~ [ide-nJ-tfies] Cos 2 x J-If- j cos2)lt ~
51-)cosltx +~osYx J =-~ - d~ + cospclo shy~os 2x middot vvy- JkoSx ~ CD~ xp
2)~C-21-- - ~ -+ eampltl x)dx = -tQn~ -2 ~ + SCDsxdx ~ I + ~05(~x)~ = amp X -+-j~S n (ax) -l- ~
-
(bYl X - ~ A+~ SihClxi + ~~ ( x d _ S x dshy
J X2ltX-t-d X -I-(X~d-+I)-
S1+~X-J)2dJ+ - )lt =- LA-+- ILt= f-
( LA- + I cik clv = dJ- [so l v e ~ 1-] ) l +uL
~ LA- ~ ~ LA --- Q
Second C0~ +U- ~ w LA--s LA-r c1LuJ ==- ~Aclu ~~ lw 1+ C plusmnoluJ= ~
shy
egtL_
~(x-) +--h~ + lX-IY +b
0-T f1~ vvo -r -c01 f == (YrJJC0 S J -+ = rygt1 -XOr-) - --rtpYl~I1--OfSI(flSOf) l~ --I- ~
(4)~vj+h -yrp~-y)dS)Y1Uur5=~Y1poundXDrS) (~)wrr-~ u-+ (+)h~q~ - ~~~
-pY1C~ -=--nyJ l) + hY) -9- - -= -rrp l1S shyi Y1 U--O~ Yl pound
7py-rv+5-t--yTYlTo) d S Y)oeLX~f5--=-~ shy_ 0 -Y) C0 db) -YVOi-5 fCjVlS
- YJ Qr1-f] -trp-c-4- _YrfJ - _ ~ II s U)q- ( shy-frp ~ - = P-c_X-~ -yrp )
X X -I] ~ tX 1- =- shyT I tJ Gf)sVor ) (iJd)
[~Jvw ~I = 0
YJh -= 11 Q
(~d f~~j-dPJ 11 1k L ~jJ JI I
hi+ t _ --yyp -e 0 CO) ~~ 7vp )( - T 1 == ( I )v---op~~~X+_I jJ IV X G =P )( + I ()
tj x~P-o ~Y1 ~ xvvap~)(~)
-U---+-(-h-t-X-)8--~-h-+-X-)--+=-lt---)-+ LY] 8 - YI 71Z -elf- Z T tIE
---nrp7r_TJh-rYJ)f - -vrplW~ ~~f -np h= Sf
fvp x -== YY(J ~
[1X -OJ- )1 lOS] 1vpxe -= -yyp - L-I1= X~ H+X==Y1
l -z z 7rp h+~Xf-5 pound
An5 lJ er-s -Iv ffuJ 0J~
=_~ =~(j)_ f X dJtshyj ~8-x2-ax
~CJlve
_---~ == ~LLf-j (~Ji) =- 0id-fj - ~JX---- - ctf J~ff j2 ~--
~l~~ - ~~-~---------
o
S-2 ciu ==- 5U--~~ ~--
- U-- + c - I ~=e - d-
LA- == -tarv- (sx) cLu- = 5 ~poundL1-(S X) dJshy
~=-~c~xJ4
2 JtOYISx) --f-~ 5
= -e - +- C -7- - ~~
-I- ~
~f=-~ -=-0 ~ -se -~e~=-~
shy~z = ~ -O=~
- 2
- LAshy3
--2~ _ ~ gt 3
middot S hcnu ~ot-+4 Yf1ecv-n V~~ ~ ~ tl-o Lj = Lj(X~ I ) (V-eA- DJ J X L
CD C~I~ ~ [) 3 J 5 j LJL cROy-y~ 7 j 0 x -=FO Cpound-vLd j poundLJ ~ A~~c-P ~
GJA (Jl =- I ( 34 ex 2 + () ~ ==- ~ 3 -I J)(2 If 3
( I rI ~---o~-d- ~J plusmn= e2)( --------------
( ~ =1 =J~(l+-~) ctu-- I raquo~
----~--~~-~~~--------~ ~~~~--------~~~cLu-- --L~
( ~u- --- L
2 Jrr~ ~~ -~------
+ ~
( -
- 1- c4 shy-------J- X~~)+5 ~-----------shy
pound
---------s4 1x +i)~--shy---------==============----j i +-u t
th~ Pr-oblevYS - tJU)
q) S~loX ~2-x~ tX-a 5In(LXJ+c
f-evieuJ
ampoJ~
CD S--J 3~X~~X4 jXl_)~ 11 dj
amp~
~) 5e2~~X~ctt
ShaLU ~oJ- fh e rYJ ecv-n Value Jh ~ frrr~cr~+o ~= Lf~) ~ [13]
I - cO5 (dLc) bull 2
SYlU= 2
r[LSe i JeNt-n esJ 1 +- Co s C~u-)L - cos
l U- =
S(I - eO(~X))(l t-~~S(~XJ) rhf
~ ~ (I - Cns2(2)lt))ctx -= ~ ~ - ~reoS(2X)dX-
- ~ ~ I + ~SC4X)~ -= - ~ 51+ ~os (4x~dx
- ~ x - 1 q S i r (tix) -t- Cshy~ 8 ~==============--____middot 6-x=~ Sh(L~) +9
( ~ k~s n lA + C ~ 4rc s ex +-~) + j~4-~~ ~ ~
copy ~ -co--n 2
6 c4 lA-~~ ~ 00vc=-d~ -7gt ~du=ampci+
~~-cnY4lA ~
d S~cu- -)amplA = d-tCAnA -dLA--4~-JX -z~~
6) == est LAshy
oLuJ = - CJ~2u-cLushy- ohu ==- C-Ll c-2u ~
-------
(sect) CD-r+ I -x - SLL V~ -) - 2 u~ + ~ ~ 3
~lt 3~0- 3 (-1) ~
SsinlXrI = (6QDs2x)~ [ide-nJ-tfies] Cos 2 x J-If- j cos2)lt ~
51-)cosltx +~osYx J =-~ - d~ + cospclo shy~os 2x middot vvy- JkoSx ~ CD~ xp
2)~C-21-- - ~ -+ eampltl x)dx = -tQn~ -2 ~ + SCDsxdx ~ I + ~05(~x)~ = amp X -+-j~S n (ax) -l- ~
-
(bYl X - ~ A+~ SihClxi + ~~ ( x d _ S x dshy
J X2ltX-t-d X -I-(X~d-+I)-
S1+~X-J)2dJ+ - )lt =- LA-+- ILt= f-
( LA- + I cik clv = dJ- [so l v e ~ 1-] ) l +uL
~ LA- ~ ~ LA --- Q
Second C0~ +U- ~ w LA--s LA-r c1LuJ ==- ~Aclu ~~ lw 1+ C plusmnoluJ= ~
shy
egtL_
~(x-) +--h~ + lX-IY +b
0-T f1~ vvo -r -c01 f == (YrJJC0 S J -+ = rygt1 -XOr-) - --rtpYl~I1--OfSI(flSOf) l~ --I- ~
(4)~vj+h -yrp~-y)dS)Y1Uur5=~Y1poundXDrS) (~)wrr-~ u-+ (+)h~q~ - ~~~
-pY1C~ -=--nyJ l) + hY) -9- - -= -rrp l1S shyi Y1 U--O~ Yl pound
7py-rv+5-t--yTYlTo) d S Y)oeLX~f5--=-~ shy_ 0 -Y) C0 db) -YVOi-5 fCjVlS
- YJ Qr1-f] -trp-c-4- _YrfJ - _ ~ II s U)q- ( shy-frp ~ - = P-c_X-~ -yrp )
X X -I] ~ tX 1- =- shyT I tJ Gf)sVor ) (iJd)
[~Jvw ~I = 0
YJh -= 11 Q
(~d f~~j-dPJ 11 1k L ~jJ JI I
hi+ t _ --yyp -e 0 CO) ~~ 7vp )( - T 1 == ( I )v---op~~~X+_I jJ IV X G =P )( + I ()
tj x~P-o ~Y1 ~ xvvap~)(~)
-U---+-(-h-t-X-)8--~-h-+-X-)--+=-lt---)-+ LY] 8 - YI 71Z -elf- Z T tIE
---nrp7r_TJh-rYJ)f - -vrplW~ ~~f -np h= Sf
fvp x -== YY(J ~
[1X -OJ- )1 lOS] 1vpxe -= -yyp - L-I1= X~ H+X==Y1
l -z z 7rp h+~Xf-5 pound
An5 lJ er-s -Iv ffuJ 0J~
=_~ =~(j)_ f X dJtshyj ~8-x2-ax
~CJlve
_---~ == ~LLf-j (~Ji) =- 0id-fj - ~JX---- - ctf J~ff j2 ~--
~l~~ - ~~-~---------
o
S-2 ciu ==- 5U--~~ ~--
- U-- + c - I ~=e - d-
LA- == -tarv- (sx) cLu- = 5 ~poundL1-(S X) dJshy
~=-~c~xJ4
2 JtOYISx) --f-~ 5
= -e - +- C -7- - ~~
-I- ~
~f=-~ -=-0 ~ -se -~e~=-~
shy~z = ~ -O=~
- 2
- LAshy3
--2~ _ ~ gt 3
middot S hcnu ~ot-+4 Yf1ecv-n V~~ ~ ~ tl-o Lj = Lj(X~ I ) (V-eA- DJ J X L
CD C~I~ ~ [) 3 J 5 j LJL cROy-y~ 7 j 0 x -=FO Cpound-vLd j poundLJ ~ A~~c-P ~
GJA (Jl =- I ( 34 ex 2 + () ~ ==- ~ 3 -I J)(2 If 3
( -
- 1- c4 shy-------J- X~~)+5 ~-----------shy
pound
---------s4 1x +i)~--shy---------==============----j i +-u t
th~ Pr-oblevYS - tJU)
q) S~loX ~2-x~ tX-a 5In(LXJ+c
f-evieuJ
ampoJ~
CD S--J 3~X~~X4 jXl_)~ 11 dj
amp~
~) 5e2~~X~ctt
ShaLU ~oJ- fh e rYJ ecv-n Value Jh ~ frrr~cr~+o ~= Lf~) ~ [13]
I - cO5 (dLc) bull 2
SYlU= 2
r[LSe i JeNt-n esJ 1 +- Co s C~u-)L - cos
l U- =
S(I - eO(~X))(l t-~~S(~XJ) rhf
~ ~ (I - Cns2(2)lt))ctx -= ~ ~ - ~reoS(2X)dX-
- ~ ~ I + ~SC4X)~ -= - ~ 51+ ~os (4x~dx
- ~ x - 1 q S i r (tix) -t- Cshy~ 8 ~==============--____middot 6-x=~ Sh(L~) +9
( ~ k~s n lA + C ~ 4rc s ex +-~) + j~4-~~ ~ ~
copy ~ -co--n 2
6 c4 lA-~~ ~ 00vc=-d~ -7gt ~du=ampci+
~~-cnY4lA ~
d S~cu- -)amplA = d-tCAnA -dLA--4~-JX -z~~
6) == est LAshy
oLuJ = - CJ~2u-cLushy- ohu ==- C-Ll c-2u ~
-------
(sect) CD-r+ I -x - SLL V~ -) - 2 u~ + ~ ~ 3
~lt 3~0- 3 (-1) ~
SsinlXrI = (6QDs2x)~ [ide-nJ-tfies] Cos 2 x J-If- j cos2)lt ~
51-)cosltx +~osYx J =-~ - d~ + cospclo shy~os 2x middot vvy- JkoSx ~ CD~ xp
2)~C-21-- - ~ -+ eampltl x)dx = -tQn~ -2 ~ + SCDsxdx ~ I + ~05(~x)~ = amp X -+-j~S n (ax) -l- ~
-
(bYl X - ~ A+~ SihClxi + ~~ ( x d _ S x dshy
J X2ltX-t-d X -I-(X~d-+I)-
S1+~X-J)2dJ+ - )lt =- LA-+- ILt= f-
( LA- + I cik clv = dJ- [so l v e ~ 1-] ) l +uL
~ LA- ~ ~ LA --- Q
Second C0~ +U- ~ w LA--s LA-r c1LuJ ==- ~Aclu ~~ lw 1+ C plusmnoluJ= ~
shy
egtL_
~(x-) +--h~ + lX-IY +b
0-T f1~ vvo -r -c01 f == (YrJJC0 S J -+ = rygt1 -XOr-) - --rtpYl~I1--OfSI(flSOf) l~ --I- ~
(4)~vj+h -yrp~-y)dS)Y1Uur5=~Y1poundXDrS) (~)wrr-~ u-+ (+)h~q~ - ~~~
-pY1C~ -=--nyJ l) + hY) -9- - -= -rrp l1S shyi Y1 U--O~ Yl pound
7py-rv+5-t--yTYlTo) d S Y)oeLX~f5--=-~ shy_ 0 -Y) C0 db) -YVOi-5 fCjVlS
- YJ Qr1-f] -trp-c-4- _YrfJ - _ ~ II s U)q- ( shy-frp ~ - = P-c_X-~ -yrp )
X X -I] ~ tX 1- =- shyT I tJ Gf)sVor ) (iJd)
[~Jvw ~I = 0
YJh -= 11 Q
(~d f~~j-dPJ 11 1k L ~jJ JI I
hi+ t _ --yyp -e 0 CO) ~~ 7vp )( - T 1 == ( I )v---op~~~X+_I jJ IV X G =P )( + I ()
tj x~P-o ~Y1 ~ xvvap~)(~)
-U---+-(-h-t-X-)8--~-h-+-X-)--+=-lt---)-+ LY] 8 - YI 71Z -elf- Z T tIE
---nrp7r_TJh-rYJ)f - -vrplW~ ~~f -np h= Sf
fvp x -== YY(J ~
[1X -OJ- )1 lOS] 1vpxe -= -yyp - L-I1= X~ H+X==Y1
l -z z 7rp h+~Xf-5 pound
An5 lJ er-s -Iv ffuJ 0J~
=_~ =~(j)_ f X dJtshyj ~8-x2-ax
~CJlve
_---~ == ~LLf-j (~Ji) =- 0id-fj - ~JX---- - ctf J~ff j2 ~--
~l~~ - ~~-~---------
o
S-2 ciu ==- 5U--~~ ~--
- U-- + c - I ~=e - d-
LA- == -tarv- (sx) cLu- = 5 ~poundL1-(S X) dJshy
~=-~c~xJ4
2 JtOYISx) --f-~ 5
= -e - +- C -7- - ~~
-I- ~
~f=-~ -=-0 ~ -se -~e~=-~
shy~z = ~ -O=~
- 2
- LAshy3
--2~ _ ~ gt 3
middot S hcnu ~ot-+4 Yf1ecv-n V~~ ~ ~ tl-o Lj = Lj(X~ I ) (V-eA- DJ J X L
CD C~I~ ~ [) 3 J 5 j LJL cROy-y~ 7 j 0 x -=FO Cpound-vLd j poundLJ ~ A~~c-P ~
GJA (Jl =- I ( 34 ex 2 + () ~ ==- ~ 3 -I J)(2 If 3
th~ Pr-oblevYS - tJU)
q) S~loX ~2-x~ tX-a 5In(LXJ+c
f-evieuJ
ampoJ~
CD S--J 3~X~~X4 jXl_)~ 11 dj
amp~
~) 5e2~~X~ctt
ShaLU ~oJ- fh e rYJ ecv-n Value Jh ~ frrr~cr~+o ~= Lf~) ~ [13]
I - cO5 (dLc) bull 2
SYlU= 2
r[LSe i JeNt-n esJ 1 +- Co s C~u-)L - cos
l U- =
S(I - eO(~X))(l t-~~S(~XJ) rhf
~ ~ (I - Cns2(2)lt))ctx -= ~ ~ - ~reoS(2X)dX-
- ~ ~ I + ~SC4X)~ -= - ~ 51+ ~os (4x~dx
- ~ x - 1 q S i r (tix) -t- Cshy~ 8 ~==============--____middot 6-x=~ Sh(L~) +9
( ~ k~s n lA + C ~ 4rc s ex +-~) + j~4-~~ ~ ~
copy ~ -co--n 2
6 c4 lA-~~ ~ 00vc=-d~ -7gt ~du=ampci+
~~-cnY4lA ~
d S~cu- -)amplA = d-tCAnA -dLA--4~-JX -z~~
6) == est LAshy
oLuJ = - CJ~2u-cLushy- ohu ==- C-Ll c-2u ~
-------
(sect) CD-r+ I -x - SLL V~ -) - 2 u~ + ~ ~ 3
~lt 3~0- 3 (-1) ~
SsinlXrI = (6QDs2x)~ [ide-nJ-tfies] Cos 2 x J-If- j cos2)lt ~
51-)cosltx +~osYx J =-~ - d~ + cospclo shy~os 2x middot vvy- JkoSx ~ CD~ xp
2)~C-21-- - ~ -+ eampltl x)dx = -tQn~ -2 ~ + SCDsxdx ~ I + ~05(~x)~ = amp X -+-j~S n (ax) -l- ~
-
(bYl X - ~ A+~ SihClxi + ~~ ( x d _ S x dshy
J X2ltX-t-d X -I-(X~d-+I)-
S1+~X-J)2dJ+ - )lt =- LA-+- ILt= f-
( LA- + I cik clv = dJ- [so l v e ~ 1-] ) l +uL
~ LA- ~ ~ LA --- Q
Second C0~ +U- ~ w LA--s LA-r c1LuJ ==- ~Aclu ~~ lw 1+ C plusmnoluJ= ~
shy
egtL_
~(x-) +--h~ + lX-IY +b
0-T f1~ vvo -r -c01 f == (YrJJC0 S J -+ = rygt1 -XOr-) - --rtpYl~I1--OfSI(flSOf) l~ --I- ~
(4)~vj+h -yrp~-y)dS)Y1Uur5=~Y1poundXDrS) (~)wrr-~ u-+ (+)h~q~ - ~~~
-pY1C~ -=--nyJ l) + hY) -9- - -= -rrp l1S shyi Y1 U--O~ Yl pound
7py-rv+5-t--yTYlTo) d S Y)oeLX~f5--=-~ shy_ 0 -Y) C0 db) -YVOi-5 fCjVlS
- YJ Qr1-f] -trp-c-4- _YrfJ - _ ~ II s U)q- ( shy-frp ~ - = P-c_X-~ -yrp )
X X -I] ~ tX 1- =- shyT I tJ Gf)sVor ) (iJd)
[~Jvw ~I = 0
YJh -= 11 Q
(~d f~~j-dPJ 11 1k L ~jJ JI I
hi+ t _ --yyp -e 0 CO) ~~ 7vp )( - T 1 == ( I )v---op~~~X+_I jJ IV X G =P )( + I ()
tj x~P-o ~Y1 ~ xvvap~)(~)
-U---+-(-h-t-X-)8--~-h-+-X-)--+=-lt---)-+ LY] 8 - YI 71Z -elf- Z T tIE
---nrp7r_TJh-rYJ)f - -vrplW~ ~~f -np h= Sf
fvp x -== YY(J ~
[1X -OJ- )1 lOS] 1vpxe -= -yyp - L-I1= X~ H+X==Y1
l -z z 7rp h+~Xf-5 pound
An5 lJ er-s -Iv ffuJ 0J~
=_~ =~(j)_ f X dJtshyj ~8-x2-ax
~CJlve
_---~ == ~LLf-j (~Ji) =- 0id-fj - ~JX---- - ctf J~ff j2 ~--
~l~~ - ~~-~---------
o
S-2 ciu ==- 5U--~~ ~--
- U-- + c - I ~=e - d-
LA- == -tarv- (sx) cLu- = 5 ~poundL1-(S X) dJshy
~=-~c~xJ4
2 JtOYISx) --f-~ 5
= -e - +- C -7- - ~~
-I- ~
~f=-~ -=-0 ~ -se -~e~=-~
shy~z = ~ -O=~
- 2
- LAshy3
--2~ _ ~ gt 3
middot S hcnu ~ot-+4 Yf1ecv-n V~~ ~ ~ tl-o Lj = Lj(X~ I ) (V-eA- DJ J X L
CD C~I~ ~ [) 3 J 5 j LJL cROy-y~ 7 j 0 x -=FO Cpound-vLd j poundLJ ~ A~~c-P ~
GJA (Jl =- I ( 34 ex 2 + () ~ ==- ~ 3 -I J)(2 If 3
f-evieuJ
ampoJ~
CD S--J 3~X~~X4 jXl_)~ 11 dj
amp~
~) 5e2~~X~ctt
ShaLU ~oJ- fh e rYJ ecv-n Value Jh ~ frrr~cr~+o ~= Lf~) ~ [13]
I - cO5 (dLc) bull 2
SYlU= 2
r[LSe i JeNt-n esJ 1 +- Co s C~u-)L - cos
l U- =
S(I - eO(~X))(l t-~~S(~XJ) rhf
~ ~ (I - Cns2(2)lt))ctx -= ~ ~ - ~reoS(2X)dX-
- ~ ~ I + ~SC4X)~ -= - ~ 51+ ~os (4x~dx
- ~ x - 1 q S i r (tix) -t- Cshy~ 8 ~==============--____middot 6-x=~ Sh(L~) +9
( ~ k~s n lA + C ~ 4rc s ex +-~) + j~4-~~ ~ ~
copy ~ -co--n 2
6 c4 lA-~~ ~ 00vc=-d~ -7gt ~du=ampci+
~~-cnY4lA ~
d S~cu- -)amplA = d-tCAnA -dLA--4~-JX -z~~
6) == est LAshy
oLuJ = - CJ~2u-cLushy- ohu ==- C-Ll c-2u ~
-------
(sect) CD-r+ I -x - SLL V~ -) - 2 u~ + ~ ~ 3
~lt 3~0- 3 (-1) ~
SsinlXrI = (6QDs2x)~ [ide-nJ-tfies] Cos 2 x J-If- j cos2)lt ~
51-)cosltx +~osYx J =-~ - d~ + cospclo shy~os 2x middot vvy- JkoSx ~ CD~ xp
2)~C-21-- - ~ -+ eampltl x)dx = -tQn~ -2 ~ + SCDsxdx ~ I + ~05(~x)~ = amp X -+-j~S n (ax) -l- ~
-
(bYl X - ~ A+~ SihClxi + ~~ ( x d _ S x dshy
J X2ltX-t-d X -I-(X~d-+I)-
S1+~X-J)2dJ+ - )lt =- LA-+- ILt= f-
( LA- + I cik clv = dJ- [so l v e ~ 1-] ) l +uL
~ LA- ~ ~ LA --- Q
Second C0~ +U- ~ w LA--s LA-r c1LuJ ==- ~Aclu ~~ lw 1+ C plusmnoluJ= ~
shy
egtL_
~(x-) +--h~ + lX-IY +b
0-T f1~ vvo -r -c01 f == (YrJJC0 S J -+ = rygt1 -XOr-) - --rtpYl~I1--OfSI(flSOf) l~ --I- ~
(4)~vj+h -yrp~-y)dS)Y1Uur5=~Y1poundXDrS) (~)wrr-~ u-+ (+)h~q~ - ~~~
-pY1C~ -=--nyJ l) + hY) -9- - -= -rrp l1S shyi Y1 U--O~ Yl pound
7py-rv+5-t--yTYlTo) d S Y)oeLX~f5--=-~ shy_ 0 -Y) C0 db) -YVOi-5 fCjVlS
- YJ Qr1-f] -trp-c-4- _YrfJ - _ ~ II s U)q- ( shy-frp ~ - = P-c_X-~ -yrp )
X X -I] ~ tX 1- =- shyT I tJ Gf)sVor ) (iJd)
[~Jvw ~I = 0
YJh -= 11 Q
(~d f~~j-dPJ 11 1k L ~jJ JI I
hi+ t _ --yyp -e 0 CO) ~~ 7vp )( - T 1 == ( I )v---op~~~X+_I jJ IV X G =P )( + I ()
tj x~P-o ~Y1 ~ xvvap~)(~)
-U---+-(-h-t-X-)8--~-h-+-X-)--+=-lt---)-+ LY] 8 - YI 71Z -elf- Z T tIE
---nrp7r_TJh-rYJ)f - -vrplW~ ~~f -np h= Sf
fvp x -== YY(J ~
[1X -OJ- )1 lOS] 1vpxe -= -yyp - L-I1= X~ H+X==Y1
l -z z 7rp h+~Xf-5 pound
An5 lJ er-s -Iv ffuJ 0J~
=_~ =~(j)_ f X dJtshyj ~8-x2-ax
~CJlve
_---~ == ~LLf-j (~Ji) =- 0id-fj - ~JX---- - ctf J~ff j2 ~--
~l~~ - ~~-~---------
o
S-2 ciu ==- 5U--~~ ~--
- U-- + c - I ~=e - d-
LA- == -tarv- (sx) cLu- = 5 ~poundL1-(S X) dJshy
~=-~c~xJ4
2 JtOYISx) --f-~ 5
= -e - +- C -7- - ~~
-I- ~
~f=-~ -=-0 ~ -se -~e~=-~
shy~z = ~ -O=~
- 2
- LAshy3
--2~ _ ~ gt 3
middot S hcnu ~ot-+4 Yf1ecv-n V~~ ~ ~ tl-o Lj = Lj(X~ I ) (V-eA- DJ J X L
CD C~I~ ~ [) 3 J 5 j LJL cROy-y~ 7 j 0 x -=FO Cpound-vLd j poundLJ ~ A~~c-P ~
GJA (Jl =- I ( 34 ex 2 + () ~ ==- ~ 3 -I J)(2 If 3
I - cO5 (dLc) bull 2
SYlU= 2
r[LSe i JeNt-n esJ 1 +- Co s C~u-)L - cos
l U- =
S(I - eO(~X))(l t-~~S(~XJ) rhf
~ ~ (I - Cns2(2)lt))ctx -= ~ ~ - ~reoS(2X)dX-
- ~ ~ I + ~SC4X)~ -= - ~ 51+ ~os (4x~dx
- ~ x - 1 q S i r (tix) -t- Cshy~ 8 ~==============--____middot 6-x=~ Sh(L~) +9
( ~ k~s n lA + C ~ 4rc s ex +-~) + j~4-~~ ~ ~
copy ~ -co--n 2
6 c4 lA-~~ ~ 00vc=-d~ -7gt ~du=ampci+
~~-cnY4lA ~
d S~cu- -)amplA = d-tCAnA -dLA--4~-JX -z~~
6) == est LAshy
oLuJ = - CJ~2u-cLushy- ohu ==- C-Ll c-2u ~
-------
(sect) CD-r+ I -x - SLL V~ -) - 2 u~ + ~ ~ 3
~lt 3~0- 3 (-1) ~
SsinlXrI = (6QDs2x)~ [ide-nJ-tfies] Cos 2 x J-If- j cos2)lt ~
51-)cosltx +~osYx J =-~ - d~ + cospclo shy~os 2x middot vvy- JkoSx ~ CD~ xp
2)~C-21-- - ~ -+ eampltl x)dx = -tQn~ -2 ~ + SCDsxdx ~ I + ~05(~x)~ = amp X -+-j~S n (ax) -l- ~
-
(bYl X - ~ A+~ SihClxi + ~~ ( x d _ S x dshy
J X2ltX-t-d X -I-(X~d-+I)-
S1+~X-J)2dJ+ - )lt =- LA-+- ILt= f-
( LA- + I cik clv = dJ- [so l v e ~ 1-] ) l +uL
~ LA- ~ ~ LA --- Q
Second C0~ +U- ~ w LA--s LA-r c1LuJ ==- ~Aclu ~~ lw 1+ C plusmnoluJ= ~
shy
egtL_
~(x-) +--h~ + lX-IY +b
0-T f1~ vvo -r -c01 f == (YrJJC0 S J -+ = rygt1 -XOr-) - --rtpYl~I1--OfSI(flSOf) l~ --I- ~
(4)~vj+h -yrp~-y)dS)Y1Uur5=~Y1poundXDrS) (~)wrr-~ u-+ (+)h~q~ - ~~~
-pY1C~ -=--nyJ l) + hY) -9- - -= -rrp l1S shyi Y1 U--O~ Yl pound
7py-rv+5-t--yTYlTo) d S Y)oeLX~f5--=-~ shy_ 0 -Y) C0 db) -YVOi-5 fCjVlS
- YJ Qr1-f] -trp-c-4- _YrfJ - _ ~ II s U)q- ( shy-frp ~ - = P-c_X-~ -yrp )
X X -I] ~ tX 1- =- shyT I tJ Gf)sVor ) (iJd)
[~Jvw ~I = 0
YJh -= 11 Q
(~d f~~j-dPJ 11 1k L ~jJ JI I
hi+ t _ --yyp -e 0 CO) ~~ 7vp )( - T 1 == ( I )v---op~~~X+_I jJ IV X G =P )( + I ()
tj x~P-o ~Y1 ~ xvvap~)(~)
-U---+-(-h-t-X-)8--~-h-+-X-)--+=-lt---)-+ LY] 8 - YI 71Z -elf- Z T tIE
---nrp7r_TJh-rYJ)f - -vrplW~ ~~f -np h= Sf
fvp x -== YY(J ~
[1X -OJ- )1 lOS] 1vpxe -= -yyp - L-I1= X~ H+X==Y1
l -z z 7rp h+~Xf-5 pound
An5 lJ er-s -Iv ffuJ 0J~
=_~ =~(j)_ f X dJtshyj ~8-x2-ax
~CJlve
_---~ == ~LLf-j (~Ji) =- 0id-fj - ~JX---- - ctf J~ff j2 ~--
~l~~ - ~~-~---------
o
S-2 ciu ==- 5U--~~ ~--
- U-- + c - I ~=e - d-
LA- == -tarv- (sx) cLu- = 5 ~poundL1-(S X) dJshy
~=-~c~xJ4
2 JtOYISx) --f-~ 5
= -e - +- C -7- - ~~
-I- ~
~f=-~ -=-0 ~ -se -~e~=-~
shy~z = ~ -O=~
- 2
- LAshy3
--2~ _ ~ gt 3
middot S hcnu ~ot-+4 Yf1ecv-n V~~ ~ ~ tl-o Lj = Lj(X~ I ) (V-eA- DJ J X L
CD C~I~ ~ [) 3 J 5 j LJL cROy-y~ 7 j 0 x -=FO Cpound-vLd j poundLJ ~ A~~c-P ~
GJA (Jl =- I ( 34 ex 2 + () ~ ==- ~ 3 -I J)(2 If 3
( ~ k~s n lA + C ~ 4rc s ex +-~) + j~4-~~ ~ ~
copy ~ -co--n 2
6 c4 lA-~~ ~ 00vc=-d~ -7gt ~du=ampci+
~~-cnY4lA ~
d S~cu- -)amplA = d-tCAnA -dLA--4~-JX -z~~
6) == est LAshy
oLuJ = - CJ~2u-cLushy- ohu ==- C-Ll c-2u ~
-------
(sect) CD-r+ I -x - SLL V~ -) - 2 u~ + ~ ~ 3
~lt 3~0- 3 (-1) ~
SsinlXrI = (6QDs2x)~ [ide-nJ-tfies] Cos 2 x J-If- j cos2)lt ~
51-)cosltx +~osYx J =-~ - d~ + cospclo shy~os 2x middot vvy- JkoSx ~ CD~ xp
2)~C-21-- - ~ -+ eampltl x)dx = -tQn~ -2 ~ + SCDsxdx ~ I + ~05(~x)~ = amp X -+-j~S n (ax) -l- ~
-
(bYl X - ~ A+~ SihClxi + ~~ ( x d _ S x dshy
J X2ltX-t-d X -I-(X~d-+I)-
S1+~X-J)2dJ+ - )lt =- LA-+- ILt= f-
( LA- + I cik clv = dJ- [so l v e ~ 1-] ) l +uL
~ LA- ~ ~ LA --- Q
Second C0~ +U- ~ w LA--s LA-r c1LuJ ==- ~Aclu ~~ lw 1+ C plusmnoluJ= ~
shy
egtL_
~(x-) +--h~ + lX-IY +b
0-T f1~ vvo -r -c01 f == (YrJJC0 S J -+ = rygt1 -XOr-) - --rtpYl~I1--OfSI(flSOf) l~ --I- ~
(4)~vj+h -yrp~-y)dS)Y1Uur5=~Y1poundXDrS) (~)wrr-~ u-+ (+)h~q~ - ~~~
-pY1C~ -=--nyJ l) + hY) -9- - -= -rrp l1S shyi Y1 U--O~ Yl pound
7py-rv+5-t--yTYlTo) d S Y)oeLX~f5--=-~ shy_ 0 -Y) C0 db) -YVOi-5 fCjVlS
- YJ Qr1-f] -trp-c-4- _YrfJ - _ ~ II s U)q- ( shy-frp ~ - = P-c_X-~ -yrp )
X X -I] ~ tX 1- =- shyT I tJ Gf)sVor ) (iJd)
[~Jvw ~I = 0
YJh -= 11 Q
(~d f~~j-dPJ 11 1k L ~jJ JI I
hi+ t _ --yyp -e 0 CO) ~~ 7vp )( - T 1 == ( I )v---op~~~X+_I jJ IV X G =P )( + I ()
tj x~P-o ~Y1 ~ xvvap~)(~)
-U---+-(-h-t-X-)8--~-h-+-X-)--+=-lt---)-+ LY] 8 - YI 71Z -elf- Z T tIE
---nrp7r_TJh-rYJ)f - -vrplW~ ~~f -np h= Sf
fvp x -== YY(J ~
[1X -OJ- )1 lOS] 1vpxe -= -yyp - L-I1= X~ H+X==Y1
l -z z 7rp h+~Xf-5 pound
An5 lJ er-s -Iv ffuJ 0J~
=_~ =~(j)_ f X dJtshyj ~8-x2-ax
~CJlve
_---~ == ~LLf-j (~Ji) =- 0id-fj - ~JX---- - ctf J~ff j2 ~--
~l~~ - ~~-~---------
o
S-2 ciu ==- 5U--~~ ~--
- U-- + c - I ~=e - d-
LA- == -tarv- (sx) cLu- = 5 ~poundL1-(S X) dJshy
~=-~c~xJ4
2 JtOYISx) --f-~ 5
= -e - +- C -7- - ~~
-I- ~
~f=-~ -=-0 ~ -se -~e~=-~
shy~z = ~ -O=~
- 2
- LAshy3
--2~ _ ~ gt 3
middot S hcnu ~ot-+4 Yf1ecv-n V~~ ~ ~ tl-o Lj = Lj(X~ I ) (V-eA- DJ J X L
CD C~I~ ~ [) 3 J 5 j LJL cROy-y~ 7 j 0 x -=FO Cpound-vLd j poundLJ ~ A~~c-P ~
GJA (Jl =- I ( 34 ex 2 + () ~ ==- ~ 3 -I J)(2 If 3
6) == est LAshy
oLuJ = - CJ~2u-cLushy- ohu ==- C-Ll c-2u ~
-------
(sect) CD-r+ I -x - SLL V~ -) - 2 u~ + ~ ~ 3
~lt 3~0- 3 (-1) ~
SsinlXrI = (6QDs2x)~ [ide-nJ-tfies] Cos 2 x J-If- j cos2)lt ~
51-)cosltx +~osYx J =-~ - d~ + cospclo shy~os 2x middot vvy- JkoSx ~ CD~ xp
2)~C-21-- - ~ -+ eampltl x)dx = -tQn~ -2 ~ + SCDsxdx ~ I + ~05(~x)~ = amp X -+-j~S n (ax) -l- ~
-
(bYl X - ~ A+~ SihClxi + ~~ ( x d _ S x dshy
J X2ltX-t-d X -I-(X~d-+I)-
S1+~X-J)2dJ+ - )lt =- LA-+- ILt= f-
( LA- + I cik clv = dJ- [so l v e ~ 1-] ) l +uL
~ LA- ~ ~ LA --- Q
Second C0~ +U- ~ w LA--s LA-r c1LuJ ==- ~Aclu ~~ lw 1+ C plusmnoluJ= ~
shy
egtL_
~(x-) +--h~ + lX-IY +b
0-T f1~ vvo -r -c01 f == (YrJJC0 S J -+ = rygt1 -XOr-) - --rtpYl~I1--OfSI(flSOf) l~ --I- ~
(4)~vj+h -yrp~-y)dS)Y1Uur5=~Y1poundXDrS) (~)wrr-~ u-+ (+)h~q~ - ~~~
-pY1C~ -=--nyJ l) + hY) -9- - -= -rrp l1S shyi Y1 U--O~ Yl pound
7py-rv+5-t--yTYlTo) d S Y)oeLX~f5--=-~ shy_ 0 -Y) C0 db) -YVOi-5 fCjVlS
- YJ Qr1-f] -trp-c-4- _YrfJ - _ ~ II s U)q- ( shy-frp ~ - = P-c_X-~ -yrp )
X X -I] ~ tX 1- =- shyT I tJ Gf)sVor ) (iJd)
[~Jvw ~I = 0
YJh -= 11 Q
(~d f~~j-dPJ 11 1k L ~jJ JI I
hi+ t _ --yyp -e 0 CO) ~~ 7vp )( - T 1 == ( I )v---op~~~X+_I jJ IV X G =P )( + I ()
tj x~P-o ~Y1 ~ xvvap~)(~)
-U---+-(-h-t-X-)8--~-h-+-X-)--+=-lt---)-+ LY] 8 - YI 71Z -elf- Z T tIE
---nrp7r_TJh-rYJ)f - -vrplW~ ~~f -np h= Sf
fvp x -== YY(J ~
[1X -OJ- )1 lOS] 1vpxe -= -yyp - L-I1= X~ H+X==Y1
l -z z 7rp h+~Xf-5 pound
An5 lJ er-s -Iv ffuJ 0J~
=_~ =~(j)_ f X dJtshyj ~8-x2-ax
~CJlve
_---~ == ~LLf-j (~Ji) =- 0id-fj - ~JX---- - ctf J~ff j2 ~--
~l~~ - ~~-~---------
o
S-2 ciu ==- 5U--~~ ~--
- U-- + c - I ~=e - d-
LA- == -tarv- (sx) cLu- = 5 ~poundL1-(S X) dJshy
~=-~c~xJ4
2 JtOYISx) --f-~ 5
= -e - +- C -7- - ~~
-I- ~
~f=-~ -=-0 ~ -se -~e~=-~
shy~z = ~ -O=~
- 2
- LAshy3
--2~ _ ~ gt 3
middot S hcnu ~ot-+4 Yf1ecv-n V~~ ~ ~ tl-o Lj = Lj(X~ I ) (V-eA- DJ J X L
CD C~I~ ~ [) 3 J 5 j LJL cROy-y~ 7 j 0 x -=FO Cpound-vLd j poundLJ ~ A~~c-P ~
GJA (Jl =- I ( 34 ex 2 + () ~ ==- ~ 3 -I J)(2 If 3
-------
(sect) CD-r+ I -x - SLL V~ -) - 2 u~ + ~ ~ 3
~lt 3~0- 3 (-1) ~
SsinlXrI = (6QDs2x)~ [ide-nJ-tfies] Cos 2 x J-If- j cos2)lt ~
51-)cosltx +~osYx J =-~ - d~ + cospclo shy~os 2x middot vvy- JkoSx ~ CD~ xp
2)~C-21-- - ~ -+ eampltl x)dx = -tQn~ -2 ~ + SCDsxdx ~ I + ~05(~x)~ = amp X -+-j~S n (ax) -l- ~
-
(bYl X - ~ A+~ SihClxi + ~~ ( x d _ S x dshy
J X2ltX-t-d X -I-(X~d-+I)-
S1+~X-J)2dJ+ - )lt =- LA-+- ILt= f-
( LA- + I cik clv = dJ- [so l v e ~ 1-] ) l +uL
~ LA- ~ ~ LA --- Q
Second C0~ +U- ~ w LA--s LA-r c1LuJ ==- ~Aclu ~~ lw 1+ C plusmnoluJ= ~
shy
egtL_
~(x-) +--h~ + lX-IY +b
0-T f1~ vvo -r -c01 f == (YrJJC0 S J -+ = rygt1 -XOr-) - --rtpYl~I1--OfSI(flSOf) l~ --I- ~
(4)~vj+h -yrp~-y)dS)Y1Uur5=~Y1poundXDrS) (~)wrr-~ u-+ (+)h~q~ - ~~~
-pY1C~ -=--nyJ l) + hY) -9- - -= -rrp l1S shyi Y1 U--O~ Yl pound
7py-rv+5-t--yTYlTo) d S Y)oeLX~f5--=-~ shy_ 0 -Y) C0 db) -YVOi-5 fCjVlS
- YJ Qr1-f] -trp-c-4- _YrfJ - _ ~ II s U)q- ( shy-frp ~ - = P-c_X-~ -yrp )
X X -I] ~ tX 1- =- shyT I tJ Gf)sVor ) (iJd)
[~Jvw ~I = 0
YJh -= 11 Q
(~d f~~j-dPJ 11 1k L ~jJ JI I
hi+ t _ --yyp -e 0 CO) ~~ 7vp )( - T 1 == ( I )v---op~~~X+_I jJ IV X G =P )( + I ()
tj x~P-o ~Y1 ~ xvvap~)(~)
-U---+-(-h-t-X-)8--~-h-+-X-)--+=-lt---)-+ LY] 8 - YI 71Z -elf- Z T tIE
---nrp7r_TJh-rYJ)f - -vrplW~ ~~f -np h= Sf
fvp x -== YY(J ~
[1X -OJ- )1 lOS] 1vpxe -= -yyp - L-I1= X~ H+X==Y1
l -z z 7rp h+~Xf-5 pound
An5 lJ er-s -Iv ffuJ 0J~
=_~ =~(j)_ f X dJtshyj ~8-x2-ax
~CJlve
_---~ == ~LLf-j (~Ji) =- 0id-fj - ~JX---- - ctf J~ff j2 ~--
~l~~ - ~~-~---------
o
S-2 ciu ==- 5U--~~ ~--
- U-- + c - I ~=e - d-
LA- == -tarv- (sx) cLu- = 5 ~poundL1-(S X) dJshy
~=-~c~xJ4
2 JtOYISx) --f-~ 5
= -e - +- C -7- - ~~
-I- ~
~f=-~ -=-0 ~ -se -~e~=-~
shy~z = ~ -O=~
- 2
- LAshy3
--2~ _ ~ gt 3
middot S hcnu ~ot-+4 Yf1ecv-n V~~ ~ ~ tl-o Lj = Lj(X~ I ) (V-eA- DJ J X L
CD C~I~ ~ [) 3 J 5 j LJL cROy-y~ 7 j 0 x -=FO Cpound-vLd j poundLJ ~ A~~c-P ~
GJA (Jl =- I ( 34 ex 2 + () ~ ==- ~ 3 -I J)(2 If 3
0-T f1~ vvo -r -c01 f == (YrJJC0 S J -+ = rygt1 -XOr-) - --rtpYl~I1--OfSI(flSOf) l~ --I- ~
(4)~vj+h -yrp~-y)dS)Y1Uur5=~Y1poundXDrS) (~)wrr-~ u-+ (+)h~q~ - ~~~
-pY1C~ -=--nyJ l) + hY) -9- - -= -rrp l1S shyi Y1 U--O~ Yl pound
7py-rv+5-t--yTYlTo) d S Y)oeLX~f5--=-~ shy_ 0 -Y) C0 db) -YVOi-5 fCjVlS
- YJ Qr1-f] -trp-c-4- _YrfJ - _ ~ II s U)q- ( shy-frp ~ - = P-c_X-~ -yrp )
X X -I] ~ tX 1- =- shyT I tJ Gf)sVor ) (iJd)
[~Jvw ~I = 0
YJh -= 11 Q
(~d f~~j-dPJ 11 1k L ~jJ JI I
hi+ t _ --yyp -e 0 CO) ~~ 7vp )( - T 1 == ( I )v---op~~~X+_I jJ IV X G =P )( + I ()
tj x~P-o ~Y1 ~ xvvap~)(~)
-U---+-(-h-t-X-)8--~-h-+-X-)--+=-lt---)-+ LY] 8 - YI 71Z -elf- Z T tIE
---nrp7r_TJh-rYJ)f - -vrplW~ ~~f -np h= Sf
fvp x -== YY(J ~
[1X -OJ- )1 lOS] 1vpxe -= -yyp - L-I1= X~ H+X==Y1
l -z z 7rp h+~Xf-5 pound
An5 lJ er-s -Iv ffuJ 0J~
=_~ =~(j)_ f X dJtshyj ~8-x2-ax
~CJlve
_---~ == ~LLf-j (~Ji) =- 0id-fj - ~JX---- - ctf J~ff j2 ~--
~l~~ - ~~-~---------
o
S-2 ciu ==- 5U--~~ ~--
- U-- + c - I ~=e - d-
LA- == -tarv- (sx) cLu- = 5 ~poundL1-(S X) dJshy
~=-~c~xJ4
2 JtOYISx) --f-~ 5
= -e - +- C -7- - ~~
-I- ~
~f=-~ -=-0 ~ -se -~e~=-~
shy~z = ~ -O=~
- 2
- LAshy3
--2~ _ ~ gt 3
middot S hcnu ~ot-+4 Yf1ecv-n V~~ ~ ~ tl-o Lj = Lj(X~ I ) (V-eA- DJ J X L
CD C~I~ ~ [) 3 J 5 j LJL cROy-y~ 7 j 0 x -=FO Cpound-vLd j poundLJ ~ A~~c-P ~
GJA (Jl =- I ( 34 ex 2 + () ~ ==- ~ 3 -I J)(2 If 3
An5 lJ er-s -Iv ffuJ 0J~
=_~ =~(j)_ f X dJtshyj ~8-x2-ax
~CJlve
_---~ == ~LLf-j (~Ji) =- 0id-fj - ~JX---- - ctf J~ff j2 ~--
~l~~ - ~~-~---------
o
S-2 ciu ==- 5U--~~ ~--
- U-- + c - I ~=e - d-
LA- == -tarv- (sx) cLu- = 5 ~poundL1-(S X) dJshy
~=-~c~xJ4
2 JtOYISx) --f-~ 5
= -e - +- C -7- - ~~
-I- ~
~f=-~ -=-0 ~ -se -~e~=-~
shy~z = ~ -O=~
- 2
- LAshy3
--2~ _ ~ gt 3
middot S hcnu ~ot-+4 Yf1ecv-n V~~ ~ ~ tl-o Lj = Lj(X~ I ) (V-eA- DJ J X L
CD C~I~ ~ [) 3 J 5 j LJL cROy-y~ 7 j 0 x -=FO Cpound-vLd j poundLJ ~ A~~c-P ~
GJA (Jl =- I ( 34 ex 2 + () ~ ==- ~ 3 -I J)(2 If 3
~CJlve
_---~ == ~LLf-j (~Ji) =- 0id-fj - ~JX---- - ctf J~ff j2 ~--
~l~~ - ~~-~---------
o
S-2 ciu ==- 5U--~~ ~--
- U-- + c - I ~=e - d-
LA- == -tarv- (sx) cLu- = 5 ~poundL1-(S X) dJshy
~=-~c~xJ4
2 JtOYISx) --f-~ 5
= -e - +- C -7- - ~~
-I- ~
~f=-~ -=-0 ~ -se -~e~=-~
shy~z = ~ -O=~
- 2
- LAshy3
--2~ _ ~ gt 3
middot S hcnu ~ot-+4 Yf1ecv-n V~~ ~ ~ tl-o Lj = Lj(X~ I ) (V-eA- DJ J X L
CD C~I~ ~ [) 3 J 5 j LJL cROy-y~ 7 j 0 x -=FO Cpound-vLd j poundLJ ~ A~~c-P ~
GJA (Jl =- I ( 34 ex 2 + () ~ ==- ~ 3 -I J)(2 If 3
S-2 ciu ==- 5U--~~ ~--
- U-- + c - I ~=e - d-
LA- == -tarv- (sx) cLu- = 5 ~poundL1-(S X) dJshy
~=-~c~xJ4
2 JtOYISx) --f-~ 5
= -e - +- C -7- - ~~
-I- ~
~f=-~ -=-0 ~ -se -~e~=-~
shy~z = ~ -O=~
- 2
- LAshy3
--2~ _ ~ gt 3
middot S hcnu ~ot-+4 Yf1ecv-n V~~ ~ ~ tl-o Lj = Lj(X~ I ) (V-eA- DJ J X L
CD C~I~ ~ [) 3 J 5 j LJL cROy-y~ 7 j 0 x -=FO Cpound-vLd j poundLJ ~ A~~c-P ~
GJA (Jl =- I ( 34 ex 2 + () ~ ==- ~ 3 -I J)(2 If 3
LA- == -tarv- (sx) cLu- = 5 ~poundL1-(S X) dJshy
~=-~c~xJ4
2 JtOYISx) --f-~ 5
= -e - +- C -7- - ~~
-I- ~
~f=-~ -=-0 ~ -se -~e~=-~
shy~z = ~ -O=~
- 2
- LAshy3
--2~ _ ~ gt 3
middot S hcnu ~ot-+4 Yf1ecv-n V~~ ~ ~ tl-o Lj = Lj(X~ I ) (V-eA- DJ J X L
CD C~I~ ~ [) 3 J 5 j LJL cROy-y~ 7 j 0 x -=FO Cpound-vLd j poundLJ ~ A~~c-P ~
GJA (Jl =- I ( 34 ex 2 + () ~ ==- ~ 3 -I J)(2 If 3
- 2
- LAshy3
--2~ _ ~ gt 3
middot S hcnu ~ot-+4 Yf1ecv-n V~~ ~ ~ tl-o Lj = Lj(X~ I ) (V-eA- DJ J X L
CD C~I~ ~ [) 3 J 5 j LJL cROy-y~ 7 j 0 x -=FO Cpound-vLd j poundLJ ~ A~~c-P ~
GJA (Jl =- I ( 34 ex 2 + () ~ ==- ~ 3 -I J)(2 If 3
