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Math Help - volume integral with 3 formulas mmn 15 3a

  1. #1
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    volume integral with 3 formulas mmn 15 3a

    find the volume inclosed by z=0 x=y and y^2+z^2=x

    i am having trouble drawing it
    i know i should look on th shadow of it on the x-y plane and integrate by it
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  2. #2
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    Quote Originally Posted by transgalactic View Post
    find the volume inclosed by z=0 x=y and y^2+z^2=x

    i am having trouble drawing it
    i know i should look on th shadow of it on the x-y plane and integrate by it
    No, you shouldn't. y^2+ z^2= x is a paraboloid with axis along the x-axis, not the y-axis. For this problem you should project onto the yz-plane.

    Or, you can just "change" the problem- swap x and y and find the voume of the region bounded by x= 0, z= y, and z= x^2+ y^2. For that, you project onto the xy-plane.
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    i cant imagine it
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  4. #4
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    I would approach it like this:
    \iint_D\int_{y^2+z^2}^{y}dxdydz where D: y^2+z^2\leq y; z\geq0
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  5. #5
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    the main problem is how to know how y^2+ z^2= x looks like
    i only know how y^2+ x^2= z
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  7. #7
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    Re: volume integral with 3 formulas mmn 15 3a

    Quote Originally Posted by HallsofIvy View Post
    No, you shouldn't. y^2+ z^2= x is a paraboloid with axis along the x-axis, not the y-axis. For this problem you should project onto the yz-plane.

    Or, you can just "change" the problem- swap x and y and find the voume of the region bounded by x= 0, z= y, and z= x^2+ y^2. For that, you project onto the xy-plane.
    i can project on every plane i want to and build the integral appropriatly
    i jast cant imagine this shape

    if i can find out how the shape looks like
    then it will solve it very fast
    but imaganening a parabaloid cutting x=0 plane and z=0
    is very hard thing to draw and imagine
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