Sample Exam #4
Math 150–Hughes
You may use a scientific calculator. Show all work.
1. Find the general indefinite integral.
a) Z3x4+4
√x+5
xdx
b) Zsec 4xtan 4xdx
c) Zsin x
cos3xdx
d) Ze1/x
x2dx
2. Evaluate the definite integral.
a) Z1
0
e−x
1+e−xdx
b) Z3
0
x
√x+1dx
3. Let F(x)=Z√x
−1
t3
(1 + t2)2dt for x≥0.
a) Find F(1).
b) Find F0(x).
4. An object moves along a line so that its velocity at time t(in
seconds) is v(t)=t2−2 (in meters per second). Find the total
distance traveled by the particle during the time period 0 ≤t≤2
(seconds).
5. Find the area of the region enclosed between the curves y=2xand
y=x3−2x.
