- Evaluate the following triple integral.

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

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

2001-12-13