Math 152 Practice for Exam 2
1. Find each antiderivative.
a)
b)
x

2
dx
4  x
x

2
x
2
 4
dx
4
2. Find each antiderivative.
x
3
 2x
a)
 ( x  1) 2
b)
 ( x  1) 2 ( x 2
dx
( x  6)
dx
 4)
3. Determine whether or not the improper integral converges. Evaluate it if it converges.
2
a)
1

x 1
dx
0

b)
1

x ( x  1)
1
2
dx

c)
1

x (ln x )
2

d)

1

e)

1
3 2
dx
1
x  ln x
1
x  ln x
dx
dx

f)
2x
 xe
dx
1

g)
5

x  x
1
3 2
dx
4. Find the length of the curve given by
t
x ( t )  e cos t
t
y ( t )  e sin t
0  t 

2
5. Find the surface area of the object formed when the curve given by
2 3
2 3
x
 y
 1 0  x  1 0  y  1 is rotated about the y-axis.
Set up the integral with respect to x and set up the integral with respect to y. Evaluate
one.
6. Which of the sequences are bounded? Which of these converge?
n
a ) {(  1 ) }
d ) {ln( n
2
b ) {cos n )}
 5 n  4 )  ln( 3 n
c ) {sec
2
1 

(1  )

n 2


) }


 4 n  6 )}
7. Which sequences are monotone increasing, decreasing? Assume n>2.
a)
( n  1 ) 

)
 sin(
2n


b)
 ln n 


 n 
c)
 e n 
 2 
 n 
8. Determine if the series converges and evaluate it if it does.

a)
 2
3
2
k 1
2 k 1
4k2

b)
  sin( n  1 )  sin n 
n0

c)

n 1
1
n(n  2)

d)
 ln( 1 
n 1
e)
 (  1)
2
n
n
2n

f )

n 1

n
2
)
n
2
2
 2n
 3n  4
 4n  n
