MA 1024 B '01 Practice Exam 3

1. Evaluate the following triple integral.

2. Set up, but do not evaluate, a double integral for the volume of the solid that lies under the surface and above the region in the plane bounded by the curves and for . Make sure you include a sketch of the region.

3. For the following integral, first sketch the domain of integration, then convert the integral to polar coordinates and evaluate the resulting integral.

4. Set up, but do not evaluate, a triple integral in cylindrical coordinates that computes the mass of a body bounded by the two surfaces and if the density is given by .

5. Use a triple integral to find the volume of the solid bounded by and the coordinate planes.

6. Compute the coordinates of the center of mass, , of a thin plate bounded by the line and the parabola if the density per unit area is . Include a sketch of the region.

William W. Farr
2001-12-13