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Math Help - Double integral help.

  1. #1
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    Double integral help.

    I want to compute.

    integral (integral D of y^2 sqrt x dA) where

    D = {x > 0, x^2 < y < 10-x^2}

    The region is basically between two parabolas. So the bounds of integration are a bit confusing.

    So y would go from 10-x^2 to x^2

    But I'm having a bit of trouble with x.

    the parabolas intersect at sqrt 5, so what would the bounds for x be? It can go from 0 to x^2 until x reaches sqrt 5 and then back to 0 from 10-x^2.
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  2. #2
    MHF Contributor Amer's Avatar
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    Re: Double integral help.

    the two curves intersect at \sqrt{5} \;\;\; -\sqrt{5} but since x>0 we are not interested with the negative point
    you are right y boundaries is the two curves, you have to draw a graph after you determine the y-boundaries make a fall to the x-axis or how i can say it see the picture
    Double integral help.-graph.jpg

    so x will change from 0 to sqrt{5}
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