Northwestern University

NetID:

Id #:

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

Math 234-0 Final Exam Spring Quarter 2013 Page 2 of 11

1. (10 points) Consider the iterated double integral

I=Z1

0Z1

√1−y

cos(x3)dx dy.

(a) Sketch the region of integration.

(b) Evaluate the double integral by reversing order of integration.

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.