(a) Find a positive continuous function f such that the area under the graph of f from 0 to t is A(t) = t2 for all t > 0.
(b) A solid is generated by rotating about the -axis the region under the curve y = f(x), where f is a positive function and x ≥0. The volume generated by the part of the curve from x = 0 to x = b is b2 for all b > 0. Find the function f.