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Math Help - calculating domain in double integral problem

  1. #1
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    calculating domain in double integral problem

    Hi,

    I have been set the following question;

    D f(x,y) dxdy, where f(x,y)=xy^2, and D is the region in the first quadrant bounded by the curves y=x^2, and x=y^2.

    The integration part I don't have a problem with, but I need some advice on how I calculate the limits from the domain statement. I assume that the answer is 0 to 1, based on common sense, but would appreciate of someone could explain how I can show the calculation of this.

    Thanks in advance.
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  2. #2
    MHF Contributor
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    Write the area of the region D as a definite integral with respect to y:

    \int_0^1 \sqrt{y}\ -\ y^2\ dy

    where the integrand is the length of any Reimann strip. Then you can easily convert that to a double integral of 1 with respect to dx dy.

    \int_0^1\ \int_{y^2}^{\sqrt{y}}\ 1\ dx\ dy

    So there's your limits.
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