Double Integral Volume Problem

  • Thread starter p3hr
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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.
 

Answers and Replies

  • #2
Dick
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You are only doing the volume in the first quadrant (where x>0). x should run from -sqrt(y) to +sqrt(y).
 
  • #3
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I had a feeling that's what was going wrong. Thank you.
 

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