a triple integral question

Nov 2009
94
6
Evaluate \(\displaystyle \int\int\int_ExydV\) where E is bounded by \(\displaystyle x=y^2, y=x^2, z=0, z=6x+y \)

My first try:
\(\displaystyle \int\int_D(\int_0^{6x+y}xydz)dA \)

\(\displaystyle =\int_0^1\int_{x^2}^{\sqrt{x}}(6x^2y+6xy^2)dydx \)
ended up with 9/14 which was incorrect.
 

chiph588@

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Champaign, Illinois
Evaluate \(\displaystyle \int\int\int_ExydV\) where E is bounded by \(\displaystyle x=y^2, y=x^2, z=0, z=6x+y \)

My first try:
\(\displaystyle \int\int_D(\int_0^{6x+y}xydz)dA \)

\(\displaystyle =\int_0^1\int_{x^2}^{\sqrt{x}}(6x^2y+6xy^2)dydx \)
ended up with 9/14 which was incorrect.
\(\displaystyle \int_0^{6x+y}xydz = 6x^2y+xy^2 \)
 
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