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Quiz #7
NAME:
#1. (6 pts) Rewrite the integral as an integral or sum of integrals with the order of operation
reversed. It is probably a good idea to sketch the region that is determined by the limits of
integration.
2
1 1 1 x
 
1
x
f ( x, y ) dy dx
3
3
#2. (8 pts) Evaluate:



0
9 x2



0
xe 2 y
dy dx
9 y
#3. Consider the integral
1
 
1 x 2
1  1 x 2

1 ( x 2  y 2 )
0
f ( x, y, z ) dz dy dx . Rewrite this as an equivalent
iterated integral by sketching the region of integration, then putting appropriate limits in the integral
below:
a. (3 pts) Sketch the region:
b. (3 pts) Complete the integral:
1
 
1 x 2
1  1 x
2

1 ( x 2  y 2 )
0
f ( x, y, z ) dz dy dx  
___
___

______
______

______
______
f ( x, y, z )dxdydz
#4.(6 pts) Write the integral
 f ( x, y, z) dV
as an iterated integral (in any order) if R is the region
R
bounded by the graphs of x  0, z  0, y  x , and z  1  y .
#5 (3 pts) Rewrite the integral as an integral or sum of integrals with the order of integration
reversed, then evaluate the integral (you may evaluate either integral).
 sin( x )
 
0
0

 y
  x  e dy dx
2
