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Triple Integrals with Cylindrical Coordinates

  1. Oct 30, 2011 #1
    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
     
  2. jcsd
  3. Oct 30, 2011 #2
    If you're integrating over the first octant, then theta doesn't go from 0 to 2pi. Other than that, the rest is ok.
     
  4. Oct 30, 2011 #3
    Thank you so much! That was the problem. I missed the part where it said the first octant.
     
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