Math 208 (Lutz) - Quiz #7, 10/18/13
Name:
Directions: This quiz has 3 questions, for a total of 20 points. Solve each problem carefully. You must
show ALL of your work in order to earn full credit.
1. (6 points) Evaluate the following integral by switching the order of integration:
! 1! 1
sin(x2 ) dx dy.
0
y
2. (6 points) Set up (but do not evaluate) an iterated (triple) integral for f (x, y, z) = xyz over the
R, where R is the region in 3-space bounded by the planes x = 0, y = 0, z = 0 and the surface
z = −x2 − y 2 + 4.
3. (8 points) Let R be the region 4 ≤ x2 + y 2 ≤ 9. Evaluate
! "
x2 + y 2 dA.
R
(Hint: Rewrite the integral in polar coordinates.)