## Area and volume (need verification)

Consider the area in the first quadrant under the curve x^2y^3=1 and to the right of x=1. By integrating from x=1 to x=b and then letting b -> infinity, show that this area is infinite, but that on revolving it about the x-axis we obtain a finite volume.

So here's my work: I integrated from 1 to b for x^(-2/3)dx and let b -> infinity which is infinity. And for volume I integrated x^(-4/3)(pi)dx from 1 to b. For this, limit as b-> infinity equals 0. So volume would be 3pi.

Is this what I was supposed to do? Thanks.