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Quiz #7
NAME:
#1. (6 pts) Rewrite the given sum of iterated integrals as a single iterated integral by reversing the
order of integration. It is probably a good idea to sketch the region that is determined by the limits
of integration.
3
x 2
 
0  4 x
4 x
4
f ( x, y ) dy dx  

1
#2. (8 pts) Evaluate:
f ( x, y ) dy dx
3  4 x



0
ex



1
y
dy dx
 ln( y)  1
#3. Consider the integral
1 1 1 y 2

0
y 0
f ( x, y, z ) dz dx dy . 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 1 y 2

0
y 0
f ( x, y, z ) dz dx dy  
___
___

______
______

______
______
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 z  x 2  y 2 and z  2   x 2  y 2  .
#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
