Math 110 Exam 1
February 28, 2008
Name
Show all work. No credit for unsupported answers.
1. “Straightforward” integrals (algebraic simplification, but no special techniques
required. No calculators.) 5 points each.
t t
A)  2 dt
t


1
B)    2  3  2 x  3 dx
x


C)  cos 2 (28 x)dx
2. Some technique(s) required. State which technique you use, and show all work.
Tables are ok. State which form is used. No calculators. 10 points each.
x2
dx
A)  2
x x
B)
2z
e
3z
dz
C)
x
2
1
dx
 8 x  17
3. (10) Find the area contained in the cardioid r  2  2 sin(  ) . Use a calculator to
do the integral, if you want.

y




x











4. A) (10) The region bounded by y  sin( x) and the x-axis on the interval [0,  ] is
revolved about the line y  3 . Show all work in setting up an integral that gives
the volume of the resulting solid. Use a calculator to evaluate your integral.
B) (10) Write an integral that gives the length of one arch of the sine curve,
from x  0 to x   . Use your calculator to evaluate the integral.

5. (20) Prove that
1
x
1
p
dx converges if p > 1, but diverges if p  1 .