Math 234 Spring 2013 Final

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15 Feb 2019
Department
Course
Professor
Northwestern University
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Math 234-0 Final Exam
Spring Quarter 2013
Tuesday, June 11, 2013
Instructions:
Mark your section.
Read each problem carefully.
Write legibly.
Show all of your work on these sheets.
The exam consists of 10 problems and 11 pages. Please verify that you have all 11
pages.
You may not use books, notes or calculators.
You have 120 minutes to complete this exam.
Problem Points Score
1 10
2 10
3 10
4 10
5 10
6 10
7 10
8 10
9 10
10 10
TOTAL 100
Section: 11AM
1PM
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Math 234-0 Final Exam Spring Quarter 2013 Page 2 of 11
1. (10 points) Consider the iterated double integral
I=Z1
0Z1
1y
cos(x3)dx dy.
(a) Sketch the region of integration.
(b) Evaluate the double integral by reversing order of integration.
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Math 234-0 Final Exam Spring Quarter 2013 Page 3 of 11
2. (10 points) Evaluate the triple integral
ZZZD
x dV
where Dthe solid region in the first octant bounded by the parabolic cylinder
z=x2and the plane y+z= 1.
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