1) Why is the integral from x=1 to x=3 of f(x)= 1/(x-2)2/3 improper?

2) When we find the area of a region bounded by an upper curve f(x) and a Lower curve g(x), we integrate f(x)-g(x). Analytically, how do we know that this integral is positive and so actually represents the area.

3) Rotate a circle of radius r around the x axis and use the method of disks to prove the formula for the volume of a sphere of radius r.

4) Describe what methods would force you to use the method of washers rather than the method of disks.