Problems

In Problems 1-10, find the length in polar coordinates.

In Problems 11-14, set up an integral for the length of the curve.

15           Show that the surface area generated by rotating the curve r = f(θ), a ≤ θ ≤ b, about

the y-axis is

(Assume 0 ≤ a < b ≤ π/2.) Show that the corresponding formula for a rotation about the x-axis is

In Problems 16-21, find the surface area generated by rotating the curve about the given axis.