January 5, 2018
5.2 Riemann Sums and Definite Integrals
Sigma Notation
fete( tz ) ott .- - + fctn ) it
→
term
E aid,¥Ea€
.at#an0
-
-
y Ak → Ktn term
�5�K= index of summation
t.ae?k#inFeFrtakyEsnEheIYtima,µ
Lower lim ,
to the upper limit ofsummation ( n )
January 5, 2018
Sigma notation examples
µ§K= I +2+3+4+5=15
£' fifkk = - 1+2-3=-2;&t¥=ia+÷iEt¥?
622£2,2→ 1 +3+5+7+9 e-
�5�E¥a⇐II,k£1f.2 (1) + b= 1
*In Ztb =/
b= - 1
Ak =1
,3
, 5,7 ,9
[
=ai*aaT←
4
L EL1 +3+5+7+9
5
=EZK - 1
÷1
EZKHk¥fk+b=_)
2C of + b= 1 L
,b= 1
2f3)tb=1
{ 2kt 7
k= -3
January 5, 2018
Algebra rules for finite sums
England.)=§l,ak±§.
,b . fifteens
N n constant→ [ Can = C. Ea .
CER multiple
k=l K=lsn ←# of terms
→ (§C=Ctct . . . +c=n .c constant
K=l - Value
an terms
Sumoflst n -
integertoN= 1 - 1 •
2=1.2
z'
N=2 - 3 : .
6=23n=3-6µg. 12=3.4
N=y - 10.
:-..
.
20=4.5
5
n=5 - 15.:iI
.
30=5.6
# -.
'. . . a
2h - l
n(n÷
January 5, 2018
The sum of the first n...
Integers:
Squares:
Cubes:
+§k=ncz#
§.
,K2=Mn+ifRn+k§k3=( nay )2
1 7
n(ntl)§3 K - K 2 z
= 3 §?,
K - { K2
k = 1
=3 (my ) . (Easy= 3 ( 1 5 3)- §1 ) ( 3 5) )= 459 - 17 8 5
= - 1 3 2 6
SequenceI
, 3,5 ,7
,9
SeriesI +3+5+7+9
HW P.
292
1,5 , 10,11-16 ,18,21 , 26,28
January 5, 2018
Riemann Sums
January 5, 2018
January 5, 2018
January 5, 2018
Find the distance traveled by the projectile with the following velocity function, from 0 to 3 seconds. (We did this already)
January 5, 2018
January 5, 2018
January 5, 2018
Start by sketching
January 5, 2018
January 5, 2018
Find the area of the shaded region
January 5, 2018
Constant functions
January 5, 2018
January 5, 2018