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Thread: Integrating within a circle?

  1. #1
    Mar 2008

    Integrating within a circle?

    Integrate \frac{\ln\left({x^{2}+y^{2}}\right)}{x^{2}+y^{2}} over the region between the circles x^{2}+y^{2}=1 and x^{2}+y^{2}=e^{2}.

    So the integration itself is fine using the quotient rule, but how do I use the circles to get the limits of integration?
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  2. #2
    MHF Contributor
    Oct 2005
    This problem works great in polar coordinates, but I think you made a typo because as written the numerator and denominator are the same.

    EDIT: I see you already noticed this.

    Ok, so in polar coordinates r^2=x^2+y^2 and the area of A(r(\theta))=\frac{1}{2} \int r^2d\theta. So now you need to express the region in terms of polar coordinates, which should be easy since r(\theta)=a is a circle with radius a.
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