Math 1B Quiz 4
7:30am — 8:20am Version V
Fri May 11, 2012
SCORE:
NAME YOU ASKED TO BE CALLED IN CLASS:
/ 30 POINTS
NO CALCULATORS ALLOWED
The region bounded by y = Vx —1 , y = x-3 and y = 0 is revolved around the line
Write, BUT DO NOT EVALUATE, a SINGLE integral for the volume of the solid.
x
=
-3.
)( j
[a]
y = x 2 and y = 4x-3
is revolved around the line
7r/
y =10.
SCORE:
/ 9 PTS
Write, BUT DO NOT EVALUATE, an integral (or sum of integrals) for the volume of the solid using the disk or washer method.
x4< -3 )e-- --4,<-1-3 -7- 0
x = I, 3
7 3 (OD- x2-5 - 00- Li-fx-.3.Vd<
(t)
[b]
/ 6 PTS
3
2_
Av
The region bounded by
SCORE:
Write, BUT DO NOT EVALUATE, an integral (or sum of integrals) for the volume of the solid using the shell method.
10
—
—
F
/Nice,
-4
).-77
J4
)(---
s9 (to
-1
(r)
3)
Math 1B Quiz 4
7:30am — 8:20am Version V
Fri May 11, 2012
SCORE:
NAME YOU ASKED TO BE CALLED IN CLASS:
/ 30 POINTS
NO CALCULATORS ALLOWED
The region bounded by y = Vx —1 , y = x-3 and y = 0 is revolved around the line
Write, BUT DO NOT EVALUATE, a SINGLE integral for the volume of the solid.
x
=
-3.
)( j
[a]
y = x 2 and y = 4x-3
is revolved around the line
7r/
y =10.
SCORE:
/ 9 PTS
Write, BUT DO NOT EVALUATE, an integral (or sum of integrals) for the volume of the solid using the disk or washer method.
x4< -3 )e-- --4,<-1-3 -7- 0
x = I, 3
7 3 (OD- x2-5 - 00- Li-fx-.3.Vd<
(t)
[b]
/ 6 PTS
3
2_
Av
The region bounded by
SCORE:
Write, BUT DO NOT EVALUATE, an integral (or sum of integrals) for the volume of the solid using the shell method.
10
—
—
F
/Nice,
-4
).-77
J4
)(---
s9 (to
-1
(r)
3)
Math 1B Quiz 4
7:30am — 8:20am Version V
Fri May 11, 2012
SCORE:
NAME YOU ASKED TO BE CALLED IN CLASS:
/ 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.
)177-71-1
SCORE:
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.
[a]
SCORE:
/ 9 PTS
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 13
D-
() O - (_4,4 -n)*7-
r-te
7
( 13-2-fxnJx
fl
k--L
[b]
/ 6 PTS
Write, BUT DO NOT EVALUATE, an integral (or sum of integrals) for the volume of the solid using the shell method.
10
Jr
ti
SINce
u>0
4.1
3-
27) (co- j)(1-
ctj
6
The base of a solid is the region bounded by y = - and y = 8
-
2x. Cross sections perpendicular to the x — axis SCORE:
/ 5 PTS
are semicircles. Write, BUT DO NOT EVALUATE, an integral (or sum of integrals) for the volume of the solid.
27(1-
C=
► ,3,
7T
Find the area between the curves y = 3
—
3x 2 and y = x 2 — 4x
—
C
x
g-ay - )•
5 over the interval 0 x
3.
SCORE:
/ 6 PTS
- 3x-=
-
K )
2
(3-3x2- (
Sz (
S
=',0(>(
x -5- -(3 -3x-L))ax
ok
clx
3
4"
( 400-2 X
-
„
x
)1
3
2
3
3
-
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
the axis of revolution if the volume of the solid is 1[ ((3
J
2
—
2
) — (3 — z y) ) dy
13.0 L'u5 pv 1 NTT
.
-A T) c.)/-)
A'S
AXiS) X
E-o(Z.
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)
6
The base of a solid is the region bounded by y = - and y = 8
-
2x. Cross sections perpendicular to the x — axis SCORE:
/ 5 PTS
are semicircles. Write, BUT DO NOT EVALUATE, an integral (or sum of integrals) for the volume of the solid.
27(1-
C=
► ,3,
7T
Find the area between the curves y = 3
—
3x 2 and y = x 2 — 4x
—
C
x
g-ay - )•
5 over the interval 0 x
3.
SCORE:
/ 6 PTS
- 3x-=
-
K )
2
(3-3x2- (
Sz (
S
=',0(>(
x -5- -(3 -3x-L))ax
ok
clx
3
4"
( 400-2 X
-
„
x
)1
3
2
3
3
-
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
the axis of revolution if the volume of the solid is 1[ ((3
J
2
—
2
) — (3 — z y) ) dy
13.0 L'u5 pv 1 NTT
.
-A T) c.)/-)
A'S
AXiS) X
E-o(Z.
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)
6
The base of a solid is the region bounded by y = - and y = 8
-
2x. Cross sections perpendicular to the x — axis SCORE:
/ 5 PTS
are semicircles. Write, BUT DO NOT EVALUATE, an integral (or sum of integrals) for the volume of the solid.
27(1-
C=
► ,3,
7T
Find the area between the curves y = 3
—
3x 2 and y = x 2 — 4x
—
C
x
g-ay - )•
5 over the interval 0 x
3.
SCORE:
/ 6 PTS
- 3x-=
-
K )
2
(3-3x2- (
Sz (
S
=',0(>(
x -5- -(3 -3x-L))ax
ok
clx
3
4"
( 400-2 X
-
„
x
)1
3
2
3
3
-
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
the axis of revolution if the volume of the solid is 1[ ((3
J
2
—
2
) — (3 — z y) ) dy
13.0 L'u5 pv 1 NTT
.
-A T) c.)/-)
A'S
AXiS) X
E-o(Z.
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)