NAMES:
MATH 152
January 28, 2015
QUIZ 1
• Show all your work and indicate your final answer clearly. You will be graded not merely
on the final answer, but also on the work leading up to it.
1. (3 points) Find the general indefinite integral.
Z 1
7
x2 + √
dx
1 − x2
Solution:
2 3
x 2 + 7 arcsin(x) + C
3
2. (3 points) Find the general indefinite integral
Z
x2014
√
dx
3
1 + x2015
Solution: Let u = 1 + x2015 . Then du = 2015 · x2014 dx so that after substituting,
Z
Z
x2014
1
du
√
√
dx =
3
3
2015
2015
u
1+x
1
3 2
=
· u3 + C
2015 2
2
3
=
(1 + x2015 ) 3 + C.
4030
NAMES:
MATH 152
3. (3 points) Find the general indefinite integral
Z
3x + sec2 (x) dx
Solution:
3x
+ tan(x) + C
ln(3)
January 28, 2015