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MA 2005 A95 Sample Exam 2 Name here
Show your work in the space provided. Unsupported answers may not
receive full credit. Use the backs of the pages if needed. (In the
real exam, there will be plenty of space for your work.)
 Evaluate the following triple integrals.

Answer:

Answer:
 Set up and evaluate a double integral in polar coordinates to find the
volume of the solid that lies under the surface z=1+x and above the
plane region bounded by the cardioid .
Answer:
 Set up and evaluate the integral for the volume of the
solid that lies under the surface z=xy and above the region
in the xy plane bounded by the curves y=x and . Make
sure you include a sketch of the region.
Answer:
 For the following integral, first sketch the region of
integration, then reverse the order of integration, and finally
evaluate the resulting integral.
Answer:
The region is bounded by the x axis, the line y=x, and the line
x=1.
 Compute the coordinates of the
center of mass, , of a thin plate bounded
by the x and y coordinate
axes and the line x+y=1 if the density per unit area is . Include a sketch of the region.
Answer:
The region is bounded by x=0, y=0, and the line y=1x.
 Use a triple integral to find the volume of the solid bounded by
the coordinate planes and the plane 2x+2y+z=2.
Answer:
 For the following integral, first sketch the domain of
integration, then convert the integral to polar coordinates and
evaluate the resulting integral.
Answer:
The region is the part of the circle in the first
quadrant.
William W. Farr
Tue Sep 19 15:17:28 EDT 1995