Final Exam Review Math 152
1. Find the volume of the solid formed if: x , y

0 , a) the region bounded by y
 b) the region bounded by y
 arctan x , and x

4
is rotated about the line y= 2. y

0 , x

3 is rotated about the y axis .
2. Determine whether or not the integral, 
0
1 ln x x
3 2 dx
, converges.
3. A semicircular tank, with radius 2 ft, is filled with water. Find the work done if all the water is pumped out a spout 2 ft above the top of the tank. The weight density of water is
62.5 pounds per cubic foot.
4. Find each antiderivative.
5 x

9 a)  x
2
( x
2 
9 ) dx b)  x
3
( x

1 )
2
( x

1 ) dx
5. Find each antiderivative. a) 
( x
2 x
2

1 )
5 2 dx x
2 b) 
( x
2 
1 )
3 2 dx

6. Find the surface area of the resulting solid. a) The curve y

2 x
3 2
3
0
 x

3
is rotated about the y -axis. b) The curve y

1 x
3
3
0
 x

1 is rotated about the x -axis.
7. Find the arc length of the curve y

2 x
3 2
0
 x

3
.
3
8. State whether or not the series converges and name the test you use. a )

 n

0 n
3 n
2


3
4 b ) n



2 n
1 ln c) n



1
(

1 ) n n tan(
1
) n d ) n



1 sin



1 n
2



9. Evaluate each series. a )

 n

0
5
2 n
(

1 ) n
3 n b ) n



2 n
2
1

1 c ) n



0
2
(

1 ) n 
2 n

1
( 2 n
2 n

1

1 )!

10. Find the Maclaurin series and give the radius of convergence and the interval of convergence. a ) b ) f ( x )
 f ( x )
 ln( x x arctan
4
 x )
2 c ) f ( x )
 x ln( 4
 x
2
)

11. a) Find the Taylor polynomial of degree 3 about a
 for f ( x )
 x sin x
.
2
b) Approximate the error if the 3rd degree Taylor polynomial is used to approximate f ( x ) on the interval
 
3
,
2

3

.
12. a) Find the volume of the parallelepiped with adjacent edges OA, OB, and OC for
A(1, 0, 1) , B(3, 4, 2), and C(2, -1, 3). b) If the base of the parallelepiped above is formed by the parallelogram with adjacent edges OA and OB, what is the height?