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Math Help - confusing integral

  1. #1
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    confusing integral

    \int^{x=1}_{x=0}\int^{y=x^{2}}_{y=\sqrt{x}} x.dx.dy

    Is this the same as

     \int^{x=1}_{x=0}x(\int^{y=\sqrt{x}}_{y=x^{2}}dy)dx

    Im a bit confused as regards how to switch the limits of integration around
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  2. #2
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    Quote Originally Posted by Tekken View Post
    \int^{x=1}_{x=0}\int^{y=x^{2}}_{y=\sqrt{x}} x.dx.dy

    Is this the same as

     \int^{x=1}_{x=0}x(\int^{y=\sqrt{x}}_{y=x^{2}}dy)dx

    Im a bit confused as regards how to switch the limits of integration around
    No, it's simply  \int^{x=1}_{x=0}x(\int_{y=\sqrt{x}}^{y=x^{2}}dy)dx .

    However, if you want to reverse the order of integration, my advice is to first draw a sketch of the region you're integrating over - have you done so?
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