Double Integral Volume Problem

[p3hr]

Homework Statement

Find the volume of the solid enclosed by the cylinders z=x^2, y=x^2, and the planes z=0 and y=4.

Homework Equations

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

1/3*[(2/5)(4)^(5/2)]

= 64/15

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.

 

[Dick]

You are only doing the volume in the first quadrant (where x>0). x should run from -sqrt(y) to +sqrt(y).

 

[p3hr]

I had a feeling that's what was going wrong. Thank you.