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Math Help - mixed variable double integral..

  1. #1
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    mixed variable double integral..

    \int_{0}^{2}\int_{\frac{1}{2}x^{2}}^{x}\frac{x}{x^  {2}+y^{2}}dydx

    how to approach
    it?
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  2. #2
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    You should reverse the order of integration...
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  3. #3
    Super Member General's Avatar
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    What is your problem exactly?

    \int \dfrac{x}{x^2+y^2} \, dy=arctan\left(\dfrac{y}{x}\right)
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  4. #4
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    but i have variables in the intervals
    ?
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  5. #5
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    Quote Originally Posted by General View Post
    What is your problem exactly?

    \int \dfrac{x}{x^2+y^2} \, dy=arctan\left(\dfrac{y}{x}\right)
    i cant solve it like this
    i ned to get rid of one integral then the other
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  6. #6
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    Why?

    \displaystyle \int_{\frac{1}{2}x^{2}}^{x}\frac{x}{x^{2}+y^{2}}dy =arctan(1)-arctan\left(\dfrac{1}{2}x\right)
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  7. #7
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    Quote Originally Posted by transgalactic View Post
    i cant solve it like this
    i ned to get rid of one integral then the other
    Yes, you can solve it like that. Just evaluate that integrand at the upper and lower limits, so that you get a function in x only- then do the second integration.
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