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Math Help - Multiple integration

  1. #1
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    Multiple integration

    Solve for a

    \int_{0}^{1}\int_{0}^{4-a-x^2}\int_{0}^{4-x^2-y}dzdydx=\frac{4}{7}

    I started it like this:

    The integration of the dz to get

    \int_{0}^{1}\int_{0}^{4-a-x^2}[4-x^2-y]dydx

    Then I integrated with respect to dy to get:

    \int_{0}^{1}[4y-x^2y-\frac{y^2}{2}]_{0}^{4-a-x^2}dx

    Then adding the limits and collecting the terms together I get:

    \int_{0}^{1}8-4x^2+a-\frac{a^2}{2}+x^4dx

    Then integrating it by dx

    [8x-\frac{4}{3}x^3+2ax-\frac{a^2x}{2}+\frac{x^5}{5}]_{0}^{1}

    Then adding the limtis

    8-\frac{4}{3}+2a-\frac{a^2}{2}+\frac{1}{5}

    Putting the terms togther and making equal \frac{4}{7}

    105a^2-420a-481=0

    I think I have gone wrong somewhere but not sure where.
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  2. #2
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    Quote Originally Posted by LL_5 View Post
    Solve for a

    \int_{0}^{1}\int_{0}^{4-a-x^2}\int_{0}^{4-x^2-y}dzdydx=\frac{4}{7}

    I started it like this:

    The integration of the dz to get

    \int_{0}^{1}\int_{0}^{4-a-x^2}[4-x^2-y]dydx

    Then I integrated with respect to dy to get:

    \int_{0}^{1}[4y-x^2y-\frac{y^2}{2}]_{0}^{4-a-x^2}dx

    Then adding the limits and collecting the terms together I get:

    \int_{0}^{1}8-4x^2+a-\frac{a^2}{2}+x^4dx

    Then integrating it by dx

    [8x-\frac{4}{3}x^3+2ax-\frac{a^2x}{2}+\frac{x^5}{5}]_{0}^{1}

    Then adding the limtis

    8-\frac{4}{3}+2a-\frac{a^2}{2}+\frac{1}{5}

    Putting the terms togther and making equal \frac{4}{7}

    105a^2-420a-481=0

    I think I have gone wrong somewhere but not sure where.
    [4y-x^2y-\frac{y^2}{2}]_{0}^{4-a-x^2}

     = 4(4-a-x^2) - x^2(4-a-x^2) - \frac{(4-a-x^2)^2}{2}

     = 16 - 4a -4x^2 - 4x^2+x^2a+x^4 - \frac{4(4-a-x^2) - a(4-a-x^2)-x^2(4-a-x^2)}{2}

     = 16 - 4a -4x^2 - 4x^2+x^2a+x^4 + \frac{-16 +4a +4x^2+ 4a-a^2-x^2a+4x^2 - ax^2 -x^4}{2}

     = 16 - 4a -4x^2 - 4x^2+x^2a+x^4 + -8 +2a +2x^2+ 2a-\frac{a^2}{2}-\frac{x^2a}{2}+2x^2 - \frac{ax^2}{2} -\frac{x^4}{2}

     = 8-4x^2-\frac{a^2}{2} +\frac{x^4}{2}

    Last edited by Mush; March 6th 2009 at 03:08 AM.
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  3. #3
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    Joined
    Nov 2008
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    So what 's the value a?

    Cos I still can't get it.

    And I think I may be wrong in the way I did this question
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