Math 1B Quiz 4 7:30am — 8:20am Version V Fri May 11, 2012

NAME YOU ASKED TO BE CALLED IN CLASS:

SCORE: / 30 POINTS

NO CALCULATORS ALLOWED

The region bounded by y=VT=7, y = x — 3 and y = 0 is revolved around the line x = -3 . Write, BUT DO NOT EVALUATE, a SINGLE integral for the volume of the solid.

SCORE: / 6 PTS

)177-71-1 I X = j 4-- 3

O 12

1J ) (C)

( 4--

The region bounded by y = x 2 and y= 4x-3 is revolved around the line y=10. SCORE: / 9 PTS

[a] Write, BUT DO NOT EVALUATE, an integral (or sum of integrals) for the volume of the solid using the disk or washer method.

- )(1--- 4x+3-0

x = I 1 3

D- () O - (_4,4 -n)*7-

r-te

7 f l ( 13-2-fxnJx k--L

[b] Write, BUT DO NOT EVALUATE, an integral (or sum of integrals) for the volume of the solid using the shell method.

10

Jr SINce u > 0

4.1

27) (co-j)(1-3 - ctj

ti

Math 1B Quiz 4 7:30am — 8:20am Version V Fri May 11, 2012

NAME YOU ASKED TO BE CALLED IN CLASS:

SCORE: / 30 POINTS

NO CALCULATORS ALLOWED

The region bounded by y = Vx —1 , y = x-3 and y = 0 is revolved around the line x = -3. Write, BUT DO NOT EVALUATE, a SINGLE integral for the volume of the solid.

SCORE: / 6 PTS

)( j

x4< -3

3

7r/ Av 2_

The region bounded by y = x 2 and y = 4x-3 is revolved around the line y =10. SCORE: / 9 PTS

[a] Write, BUT DO NOT EVALUATE, an integral (or sum of integrals) for the volume of the solid using the disk or washer method.

)e-- --4,<-1-3 -7- 0 x = I, 3

7 3 (OD- x2-5 - 00- Li-fx-.3.Vd<

(t)

[b] Write, BUT DO NOT EVALUATE, an integral (or sum of integrals) for the volume of the solid using the shell method.

10

/Nice,

-4 )(--- J- 4 3)

).-77 s9 (to -1 (r) n

— — F

Math 1B Quiz 4 7:30am — 8:20am Version V Fri May 11, 2012

NAME YOU ASKED TO BE CALLED IN CLASS:

SCORE: / 30 POINTS

NO CALCULATORS ALLOWED

The region bounded by y = Vx —1 , y = x-3 and y = 0 is revolved around the line x = -3. Write, BUT DO NOT EVALUATE, a SINGLE integral for the volume of the solid.

SCORE: / 6 PTS

)( j

x4< -3

3

7r/ Av 2_

The region bounded by y = x 2 and y = 4x-3 is revolved around the line y =10. SCORE: / 9 PTS

[a] Write, BUT DO NOT EVALUATE, an integral (or sum of integrals) for the volume of the solid using the disk or washer method.

)e-- --4,<-1-3 -7- 0 x = I, 3

7 3 (OD- x2-5 - 00- Li-fx-.3.Vd<

(t)

[b] Write, BUT DO NOT EVALUATE, an integral (or sum of integrals) for the volume of the solid using the shell method.

10

/Nice,

-4 )(--- J- 4 3)

).-77 s9 (to -1 (r) n

— — F

The base of a solid is the region bounded by y = -6

and y = 8 - 2x. Cross sections perpendicular to the x — axis SCORE:

are semicircles. Write, BUT DO NOT EVALUATE, an integral (or sum of integrals) for the volume of the solid.

/ 5 PTS

C= 27(1-

►,3,

7T C g-ay - )• x

Find the area between the curves y = 3 — 3x 2 and y = x 2 — 4x — 5 over the interval 0 x 3. SCORE:

/ 6 PTS

- 3 x - =

-

2

K )

(3-3x2- (

Sz ( x -5- -(3 -3x-L))ax

S clx ok

X - „ x =',0(>( 4" (400-2 )1 3 3 2- 3 3

2 2 the axis of revolution if the volume of the solid is 1[J ((3 — ) — (3 — z y) ) dy .

A solid is created by revolving a region around an axis of revolution. Sketch the region and find the equation of SCORE: / 4 PTS 4

13.0 L'u5 pv 1 NTT

-A T) c.)/-)

A'S

E-o(Z. AXiS) X

tA tA

S 1- 1-rtOj c c_e) 2-► 2-ECT (2.Z-0 ot-i

t p2 S D M El+-o P4 DtcPrr)

The base of a solid is the region bounded by y = -6

and y = 8 - 2x. Cross sections perpendicular to the x — axis SCORE:

are semicircles. Write, BUT DO NOT EVALUATE, an integral (or sum of integrals) for the volume of the solid.

/ 5 PTS

C= 27(1-

►,3,

7T C g-ay - )• x

Find the area between the curves y = 3 — 3x 2 and y = x 2 — 4x — 5 over the interval 0 x 3. SCORE:

/ 6 PTS

- 3 x - =

-

2

K )

(3-3x2- (

Sz ( x -5- -(3 -3x-L))ax

S clx ok

X - „ x =',0(>( 4" (400-2 )1 3 3 2- 3 3

2 2 the axis of revolution if the volume of the solid is 1[J ((3 — ) — (3 — z y) ) dy .

A solid is created by revolving a region around an axis of revolution. Sketch the region and find the equation of SCORE: / 4 PTS 4

13.0 L'u5 pv 1 NTT

-A T) c.)/-)

A'S

E-o(Z. AXiS) X

tA tA

S 1- 1-rtOj c c_e) 2-► 2-ECT (2.Z-0 ot-i

t p2 S D M El+-o P4 DtcPrr)

The base of a solid is the region bounded by y = -6

and y = 8 - 2x. Cross sections perpendicular to the x — axis SCORE:

are semicircles. Write, BUT DO NOT EVALUATE, an integral (or sum of integrals) for the volume of the solid.

/ 5 PTS

C= 27(1-

►,3,

7T C g-ay - )• x

Find the area between the curves y = 3 — 3x 2 and y = x 2 — 4x — 5 over the interval 0 x 3. SCORE:

/ 6 PTS

- 3 x - =

-

2

K )

(3-3x2- (

Sz ( x -5- -(3 -3x-L))ax

S clx ok

X - „ x =',0(>( 4" (400-2 )1 3 3 2- 3 3

2 2 the axis of revolution if the volume of the solid is 1[J ((3 — ) — (3 — z y) ) dy .

A solid is created by revolving a region around an axis of revolution. Sketch the region and find the equation of SCORE: / 4 PTS 4

13.0 L'u5 pv 1 NTT

-A T) c.)/-)

A'S

E-o(Z. AXiS) X

tA tA

S 1- 1-rtOj c c_e) 2-► 2-ECT (2.Z-0 ot-i

t p2 S D M El+-o P4 DtcPrr)