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Math Help - another triple integration!

  1. #1
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    Question another triple integration!

    Use a triple integral to find the volume of the solid bounded by the surface y=x^2 and the planes y+z=4 and z=0.

    Thank you very much.
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  2. #2
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    Try this:

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

    Here's a haphazard attempt at a graph of your region. I hope it gives you some idea of what it looks like.
    Last edited by galactus; November 24th 2008 at 05:39 AM.
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  3. #3
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    Hi galactus,

    Thank you very much.

    Why is the integration of dy from x^2 to 4 ?
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  4. #4
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    Hello kittykat:

    Because that's where the plane 'slices' the parabola x^2.

    Here's a graph. The line y=4 is where the plane z=4-y meets the parabola.

    So, you integrate over y from x^2 to 4. See?.

    At x=2, y=x^2=4

    The 3-D I posted is rather cock-eyed, but you can see it there.

    I gonna go mow grass now, so I may not be back for a few hours.
    Last edited by galactus; November 24th 2008 at 05:39 AM.
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  5. #5
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    " I gonna go mow grass now, so I may not be back for a few hours. "

    Enjoy the green and beautiful grass!
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  6. #6
    Eater of Worlds
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    Actually, it's rather hot here in PA today.

    Did you follow what I attempted to explain?.
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  7. #7
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    Not really, I am still thinking ....

    I am very bad in visualize the 3D objects. Thus , it is so how difficult for me to set up the integrals for triple integration.


    Thanks! I got it now!
    Last edited by kittycat; August 25th 2007 at 11:04 AM.
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  8. #8
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    First, try drawing your parabola y=x^2. That's easy enough. It's the plane rising up the z-axis that's the booger to visualize. Try plotting various points for it.

    z=4-y, if y=0, z=4

    If y=4, z=0. See there?. That's where the plane intersects the parabola in the xy plane.

    Then it rises up the z-axis at a slant and intersects the z axis at y=0.
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