Math 129 Name______________________________________
Test 5
1. Evaluate the
following indefinite integrals. (6
pts each)
a. 
b. 
c. 
d. 
Use
substitution.
2. Find 
if 
, 
and 
. (6 pts)
3. Let f(x) = 1 - 2x. Calculate the definite integral 
by finding the
limit of an appropriate 
(6
pts)
4. Evaluate the following definite integrals
using the Fundamental Theorem of Calculus. (6 pts each)
a. 
b. 
Use substitution.
c. 
Use
substitution.
5. Find the area of
the region bounded by 
and the 
axis. (6 pts)
6. a. Find the average value of 
on the interval 
. (5 pts)
b. Find 
(5
pts)
7. Use either the
Trapezoid Rule or
1. Differentiate the following. (5 pts each)
a. y = 
b. 
c. 
d. 
e. 
2. Evaluate the following. (5 pts each)
a. 
b. 
c. 
d. 
e. 
Bonus questions worth 3 points each.
B1. Evaluate
.
B2. Evaluate
. Hint: Rewrite the numerator as 
.
B3. Evaluate 
B4. Determine if 
satisfies the
differential equation 
.