Change of Coordinates (7 problems)

Use cylindrical coordinates to compute the integral

where Q is the cylindrical solid given by

Use Jacobian to evaluate

where R is the triangular region in the first octant bounded between. Use

Using polar coordinates to find the volume of the given solid: Above the coneand below the sphere.

Use polar coordinates to find the volume of the solid bounded by the paraboloid, and the plane in the first quadrant

Compute the following iterated integral using polar coordinates:

Electric charge is distributed on the disk, so that the charge density at the pointis . Compute the total charge over the disk.

Use polar coordinates to evaluate, where R is the region bounded by the circlesand.