Find the volume of the solid enclosed by the cylinders z=x^2, y=x^2, and the planes z=0 and y=4.
The Attempt at a Solution
∫∫ x^2 dA
For the limits of integration, I obtained y=x^2 and y=4, x=0 and x=2
I changed the order of integration and obtained x=y^(1/2) and x=0, y=0 and y=4.
∫0 to 4 ∫0 to y^(1/2) x^2 dxdy
(1/3) * ∫0 to 4 (y^(3/2)) dy
I am not sure where I am going wrong. The back of the book says it's 128/15 though. In fact, for a few problems I've got (1/2)*the correct answer for these problems.