Results 1 to 2 of 2

Thread: Integrating within a circle?

  1. #1
    Mar 2008

    Integrating within a circle?

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

    So the integration itself is fine using the quotient rule, but how do I use the circles to get the limits of integration?
    Follow Math Help Forum on Facebook and Google+

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

Similar Math Help Forum Discussions

  1. Integrating a circle with rectangular elements
    Posted in the Calculus Forum
    Replies: 1
    Last Post: Aug 3rd 2010, 08:58 PM
  2. Replies: 6
    Last Post: Jul 8th 2010, 05:39 PM
  3. Replies: 7
    Last Post: Mar 15th 2010, 04:10 PM
  4. Replies: 2
    Last Post: Feb 6th 2010, 08:31 AM
  5. Replies: 0
    Last Post: Oct 12th 2008, 04:31 PM

Search Tags

/mathhelpforum @mathhelpforum