Some integration practice:

1) Given a disk of radius R whose surface charge density eta=br, where b is a constant and r is the distance from the center:
(a) Find the total charge on the disk.
(b) Find the electric field a distance z above the center of the disk. (Warning: this is not a very pretty expression.)
(c) Does your answer to (b) give what you expect when z>>R? (Now, this is a challenge problem! I would be thrilled to pieces if you can do this part of the problem.)

2) Suppose the linear charge density of a ring of radius R is given by lambda=b sin(theta). What is the electric field at the center of the ring?

3) Consider a sphere of radius R. It contains a total charge Q, with the charge density varying linearly with radius, from zero at the surface to a maximum value at the center of the sphere. What is the electric field everywhere due to this charge distribution?