#### Problem 1P

a Find a positive continuous function f such that the area under the graph of f from 0 to t is A(t)=t3 for all t0. b A solid is generated by rotating about the x-axis the region under the curve y=f(x), where f is a positive function and x0. The volume generated by the part of the curve from x=0 to x=b is b2 for all b0. Find the function f.