21B Final Review Problems
1)
x
3
+
6
x
2
+
2
x
+
3
x
2
+
6
x
+
1
dx
!
"
#
2)
x
+
1
x
4
+
x
2
dx
!
"
#
3)
ln(2
x
)
x
2
dx
!
"
#
4)
1
x
3
+
1
dx
!
"
#
5)
x
3
4
!
x
2
dx
"
#
$
6)
dx
x
4
x
2
!
9
"
#
$
7) Converge or diverge?
a)
x
x
4
+
1
0
!
"
#
$
dx
b)
2
+
cos
x
x
!
"
#
$
%
dx
c)
1
x
ln
x
1
e
!
"
#
dx
8) Let R be the region under the first “arch” of
y
=
sin
x
and above the
x
axis from
0,
[ ]
.
a) Find the volume of the solid formed by revolving R about the
x
axis.
b) Findthe volume of the solid formed by revolving R about the
y
axis.
c) SET UP an integral for the volume when R is revolved about the line
x
=
2
.
9) SET UP an integral for the area bounded by the graphs of
x
=
y
2
and
x
=
y
+
6
.
10) Find the centroid of the region bounded by
y
=
x
4
and
y
=
1
. Assume constant density.
11) A vertical dam 4
ft
tall is in the shape of an isosceles trapezoid with the top of the dam 10
ft
across and the bottom 4
ft
across. SET UP an
integral for the total force on the dam at full capacity. (
water
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This note was uploaded on 05/26/2011 for the course MATH 16B taught by Professor Sarason during the Spring '06 term at Berkeley.
 Spring '06
 Sarason
 Calculus

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