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Quiz #5
NAME:
#1(5 pts) Rewrite the given integral as an integral or sum of integrals with the order of integration
reversed.
9
y

f ( x, y ) dx dy
0 0
#2(6 pts) Write
 f ( x, y, z) dV as an iterated integral in rectangular coordinates, where D is the
D
set in the first octant bounded by the graphs of x  0, y  0, z  1, and x  y  z  2.
#3(6 pts) Rewrite

4  x 2  y 2 dA using polar coordinates, where D is the region in the first
D
quadrant bounded by the graphs of y  x, x 2  y 2  4, and (x  1)2  y 2  1 (below the line y  x ).
Sketch the region D.
#4(6 pts) Write the triple integral

  2 
D
coordinates given that D  ( x, y, z )

x 2  y 2 dV as an iterated integral in cylindrical

x2  y 2  z  3
(2 x  y  3) 2
D (2 y  x  6)2 dA into an
integral that is easily evaluated where D is the square region shown below.
#5(8 pts) Use an appropriate change of variables to convert the integral
#6(2 pts) Determine whether
 1  x
3
2
1
dV converges or diverges.
 y2  z2 
[If you’re not sure what to do with this, discuss, in general, how you might determine whether
3
 f ( x, y, z) dV converges given that f ( x, y, z)  0 on ]
3