Problem 1

Determine the value of the integral

Problem 2

Using the maxima and minima of the function, produce upper and lower estimates of the integral where is the circular disk .

Problem 3

Find a polar equation of the form for the curve represented by the Cartesian equation .

Problem 4

Consider the solid under the graph above the disk , where .

(a)

Set up the integral to find the volume of the solid

(b)

Evaluate the integral and find the volume. Your answer will be in terms of .

Problem 5

By changing to polar coordinates, evaluate the integral where is the disk .