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Practice Questions for Math 132 Exam 2 - Prof. Lynda L. Ballou, Exams of Analytical Geometry and Calculus

Practice questions for exam 2 in math 132. The questions cover various topics such as integration, differentiation, and finding areas and volumes of revolution. Students are expected to evaluate integrals, find antiderivatives, and apply the fundamental theorem of calculus.

Typology: Exams

Pre 2010

Uploaded on 08/08/2009

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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
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 xaxis.
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
+∞
+

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Download Practice Questions for Math 132 Exam 2 - Prof. Lynda L. Ballou and more Exams Analytical Geometry and Calculus in PDF only on Docsity!

Practice Questions for Exam 2 Math 132 L.Ballou

  1. Evaluate

2

2 3/ 2 (4 )

x dxx

  1. Evaluate

3 2 cos x sin x dx

  1. Evaluate x sec x tan x dx
  1. Evaluate

2

3

x x dx x x

  1. Evaluate 2 2 1

dx

x x +

  1. Evaluate

4 2 tan x sec x dx

  1. Evaluate

3 2

2

x x dx x x

  1. Evaluate

2 sin 3

x e xdx

  1. Find the area of the surface generated by revolving the curve y = ln x from x = 1 to x = e about the

y -axis.

  1. The region in the first quadrant enclosed by the coordinate axis, the curve

x y = e and the line x = 1 is

revolved about the y -axis to generate a solid. Find the volume of the solid.

  1. Let R be the region in the first quadrant that is bounded above by the line (^) y = 1 , below by the curve

y = ln x and on the left by x = 1. Find the volume of the solid generated by revolving the region R

about the x –axis.

  1. Solve the initial value problem

2 4

dy x x dx

= − for x ≥ 2 where y ( 2 )= 0

13. Solve the initial value problem ( )

4 2 3 4 1 2 3

dy x x dx

+ + = where ( )

y

  1. Use integration, the Direct Comparison Test or the Limit Comparison Test to test if the following

integral convergence.

3/

4

dx x

  1. Determine if the following integral converges or diverges. If it converges evaluate the integral.

2

1

dx x

+∞