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Math Help - a triple integral question

  1. #1
    Member Em Yeu Anh's Avatar
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    Nov 2009
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    Red face a triple integral question

    Evaluate \int\int\int_ExydV where E is bounded by x=y^2, y=x^2, z=0, z=6x+y

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

    =\int_0^1\int_{x^2}^{\sqrt{x}}(6x^2y+6xy^2)dydx
    ended up with 9/14 which was incorrect.
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  2. #2
    MHF Contributor chiph588@'s Avatar
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    Champaign, Illinois
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    Quote Originally Posted by Em Yeu Anh View Post
    Evaluate \int\int\int_ExydV where E is bounded by x=y^2, y=x^2, z=0, z=6x+y

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

    =\int_0^1\int_{x^2}^{\sqrt{x}}(6x^2y+6xy^2)dydx
    ended up with 9/14 which was incorrect.
     \int_0^{6x+y}xydz = 6x^2y+xy^2
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  3. #3
    Member Em Yeu Anh's Avatar
    Joined
    Nov 2009
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    Quote Originally Posted by chiph588@ View Post
     \int_0^{6x+y}xydz = 6x^2y+xy^2
    *sigh* I'm so careless. Thanks!
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