(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Evaluate the integral, where E is the solid in the first octant that lies beneath the paraboloid z = 9 - x2 - y2.

∫∫∫(2(x^3+xy^2))dV

2. Relevant equations

x=rcosθ

y=rsinθ

x^2+y^2=r^2

3. The attempt at a solution

θ=0 to 2π, r=0 to 3, z=0 to (9-r^2)

2(x^3+xy^2)=2x(x^2+y^2)=2rcos(θ)(r^2)

∫0 to 2π ∫0 to 3 ∫0 to (9-r^2) (2rcos(θ)r^2)rdzdrdθ

I was wondering if my bounds were correct. And when I solved the integral I keep getting an answer of 0, which is incorrect. Can someone please help me with this problem?

1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution

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# Triple Integrals with Cylindrical Coordinates

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