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Math Help - Calculate volume

  1. #1
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    Calculate volume

    The volume of solid limited by: 2y^2=x, \frac{x}{4}+\frac{y}{2}+\frac{z}{4}=1, z=0 and y=0


    Answer:
    \frac{17}{5}
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  2. #2
    MHF Contributor Mathstud28's Avatar
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    Quote Originally Posted by Apprentice123 View Post
    The volume of solid limited by: 2y^2=x, \frac{x}{4}+\frac{y}{2}+\frac{z}{4}=1, z=0 and y=0


    Answer:
    \frac{17}{5}
    Maybe I am making a computational error but I keep getting \frac{81}{5}.
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  3. #3
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    \int_{0}^{1}\int_{2y^{2}}^{4-2y}(-x-2y+4)dxdy

    \int_{0}^{1}\int_{2y^{2}}^{4-2y}\int_{0}^{-x-2y+4}dzdxdy

    Now, try doing it by switching the limits of integration.
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  4. #4
    MHF Contributor Mathstud28's Avatar
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    Quote Originally Posted by galactus View Post
    \int_{0}^{1}\int_{2y^{2}}^{4-2y}(-x-2y+4)dxdy

    \int_{0}^{1}\int_{2y^{2}}^{4-2y}\int_{0}^{-x-2y+4}dzdxdy

    Now, try doing it by switching the limits of integration.
    Ahh thank you very much Galctus! I had \int_{-2}^{1}\cdots for some reason haha

    EDIT: I see what I did, I solved the inequality wrong by mistake. It's good now.
    Last edited by Mathstud28; November 8th 2008 at 10:29 AM.
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  5. #5
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    thank you very much
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  6. #6
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    There is a "tutorial" to build the graphic.
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  7. #7
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    Quote Originally Posted by Mathstud28 View Post
    Ahh thank you very much Galctus! I had \int_{-2}^{1}\cdots for some reason haha

    EDIT: I see what I did, I solved the inequality wrong by mistake. It's good now.

    2y^2=x A parable

    \frac{x}{4}+\frac{y}{2}+\frac{z}{4}=1 What is this graphic?
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  8. #8
    MHF Contributor Mathstud28's Avatar
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    Quote Originally Posted by Apprentice123 View Post
    2y^2=x A parable

    \frac{x}{4}+\frac{y}{2}+\frac{z}{4}=1 What is this graphic?
    If I am understanding you correctly, a plane.
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  9. #9
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    Quote Originally Posted by Mathstud28 View Post
    If I am understanding you correctly, a plane.

    Thank you. Why the integral range from 0 to 1?
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  10. #10
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    Why not?

    \int_{0}^{2} \int_{2y^2}^{4-2y} \int_{0}^{4-x-2y}dzdxdy
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