MVC
Chapter 5 Quiz
NAME:
Instructions: Though a calculator is allowed, you must show all steps leading to your answer.
SHOW ALL WORK !!
#1. Evaluate the following integral (show all steps in calculating integral by hand):
1 x
 e
x2
dy dx
0 0
#2. Rewrite the integral as an integral or sum of integrals with the order of integration reversed.
You need not (should not) evaluate the integral.
l ey

0 y
MVC
F ( x, y ) dx dy
#3. Rewrite

4  x 2  y 2 dA using polar coordinates, where D is the region in the first quadrant
D
bounded by the graphs of y  0, y  x, and x 2  y 2  4 .
#4. Write
 f ( x, y, z) dV as an iterated integral in rectangular coordinates, where D is the set in
D
the first octant bounded by the graphs of y  2 x 2 and y  4 z  8.
MVC
2 x
#5 Calculate
  ( x  y) dy dx , by making the change of variables
0 0
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x  u  v and y  u  v.
#6. Look at the integral
  x
2
 y 2  dV where D is the region above the plane z  0 , inside the
D
sphere x  y  z  4 , and outside the cone z  x 2  y 2 .
2
2
2
a. Write this integral as an iterated integral (or integrals) in cylindrical coordinates.
b. Write this integral as an iterated integral (or integrals) in spherical or rectangular
coordinates (your choice).
MVC
Concepts
1
#7. Convert the integral

1 x
0
transformation x  u  uv, y  uv .
MVC
1
y ln(4  x  y ) dy dx to an integral in u and v using the