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Homework Help: Triple Integral in Cylindrical Coordinates

  1. Nov 9, 2008 #1
    1. The problem statement, all variables and given/known data
    Evaluate [tex]\int \int \int_E x^2 \, dV[/tex] where E is the solid that lies within the cylinder [tex]x^2+y^2=1[/tex], above the plane [tex]z=0[/tex], and below the cone [tex]z^2=4x^2+4y^2[/tex].

    2. Relevant equations
    In cylindrical coordinates, [tex]x^2+y^2=r^2[/tex] and [tex]x=r\cos{\theta}[/tex].

    3. The attempt at a solution
    I tried [tex]\int _0^{2\pi }\int _0^1\int _{-2r}^{2r}r^2 cos^2\theta\;\;r\;\;dzdrd\theta[/tex] but I must have messed up the bounds somehow.

    Any ideas?
  2. jcsd
  3. Nov 10, 2008 #2


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    Science Advisor
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    Hi daveyman! :smile:

    z goes from zero to 2r. :wink:
  4. Nov 10, 2008 #3
    Of course - it says it right in the problem :-) Thanks!
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