Practice Questions for Exam 2 Math 132 L.Ballou
1. Evaluate
2
2 3/2
(4 )
xdx
x−
⌠
⌡
.
2. Evaluate
32
cos sinx xdx
∫
3. Evaluate
sec tanx x x dx
∫
4. Evaluate
2
3
83
3
xx
dx
xx
+−
+
⌠
⌡
.
5. Evaluate
22
1
dx
xx+
⌠
⌡
6. Evaluate
42
tan secx xdx
∫
7. Evaluate
32
2
4
43
xx
dx
xx
+
++
⌠
⌡
8. Evaluate
2
sin3
x
e xdx
−
∫
.
9. Find the area of the surface generated by revolving the curve
lnyx=
from
1x=
to
xe=
about the
y-axis.
10. The region in the first quadrant enclosed by the coordinate axis, the curve
x
ye=
and the line
1x=
is
revolved about the y-axis to generate a solid. Find the volume of the solid.
11. Let R be the region in the first quadrant that is bounded above by the line
1y=
, below by the curve
lnyx=
and on the left by
1x=
. Find the volume of the solid generated by revolving the region R
about the x–axis.
12. Solve the initial value problem
24
dy
xx
dx = −
for
2x≥
where
( )
20y=
13. Solve the initial value problem
( )
42
3 4 1 23
dy
xx dx
++ =
where
( )
3
14
y
π
= −
14. Use integration, the Direct Comparison Test or the Limit Comparison Test to test if the following
integral convergence.
3/2
4
2
1dx
x
∞
−
⌠
⌡
15. Determine if the following integral converges or diverges. If it converges evaluate the integral.
2
1
1
(3 2) dx
x
+∞
+
⌠
⌡