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Math Exam 1 - Integration and Volumes - Prof. Andrew M. Diener, Exams of Calculus

Christian Brothers University (CBU)Calculus
Prof. Andrew M. Diener

A math exam from math 132, held on february 12, 2009. The exam covers various topics related to integration and finding volumes of solids of revolution. It includes questions on finding integrals, using simpson's rule, and calculating volumes of solids created by rotating regions around axes.

Typology: Exams

Pre 2010

Uploaded on 08/16/2009

koofers-user-9wy
koofers-user-9wy 🇺🇸

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EXAM 1
Math 132
February 12, 2009
Name
1. Find each of the following integrals. No credit will be given for a correct answer which has
no supporting arguments. (No, the statement “I used the calculator” is NOT a supporting
argument.) (9 pts each)
(a) Zcos (x)
psin (x)dx.
(b) Zz2cos (z3)dz.
(c) Z2x3
√1−x4dx.
(d) Z2
0
ex
1 + e2xdx.
pf3
pf4

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EXAM 1

Math 132 February 12, 2009

Name

  1. Find each of the following integrals. No credit will be given for a correct answer which has no supporting arguments. (No, the statement “I used the calculator” is NOT a supporting argument.) (9 pts each)

(a)

cos (x) √ sin (x)

dx.

(b)

z^2 cos (z^3 ) dz.

(c)

2 x^3 √ 1 − x^4

dx.

(d)

0

ex 1 + e^2 x^

dx.

(e)

0

x^2

x^2 + 9 dx

  1. Use the Simpson’s Rule with n = 8 to estimate the numerical value of

2

x

dx. Find an

upper bound for the error in your estimate. (10 pts)

  1. Find the volume created by rotating the region bounded by y^2 = x, y = 2 and x = 0 around the x-axes. (8 pts)
  1. A church steeple is 30 feet tall with square cross sections. The square at the base has side 3 feet, and the square at the top has side 6 inches. Assume that the length of the sides varies from the bottom to the top in a linear fashion. Compute the volume of the church steeple. (8 pts)
  2. Write the integral needed to find the length of the curve y = ln (x) for 1 ≤ x ≤ 4. (7 pts)