Let f be a nonnegative function with a continuous first derivative on [a, b] and suppose that

Question:

Let f be a nonnegative function with a continuous first derivative on [a, b] and suppose that g(x) = cf(x) and h(x) = f(cx), where c > 0. When the curve y = f(x) on [a, b] is revolved about the x-axis, the area of the resulting surface is A. Evaluate the following integrals in terms of A and c.

a. Г | 2тg(») Ve + 8 ()? dn a