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Simple integration

  1. Dec 29, 2009 #1
    Just started learning integration, and although I can manage simple stuff, I've run into problems with some experiments of mine.

    http://enes.fi/temp/circle.png [Broken]

    The function for a circle is:

    [itex]y = \sqrt{r^{2} - x^{2}}[/itex]

    ; and Wolfram gives the integral as:

    [itex]\frac{1}{2}\left[x \cdot \sqrt{r^{2} - x^{2}} + r^{2} \cdot tan^{-1} \left(\frac{x}{\sqrt{r^{2} - x^{2}}}\right)\right][/itex]

    This in turn results in:

    [itex]f(b) - f(a) = f(s) - 0[/itex]

    However, it's all wrong!

    A radius of 10 means the area is approximately 78.540. Plugging in 10 into the equation results in division by zero. Even trying to integrate from 0 to 1, I get an area of 291.934, when it should be slightly less than 10!

    Grrr! What am I doing wrong?
    Last edited by a moderator: May 4, 2017
  2. jcsd
  3. Dec 29, 2009 #2
    you have to take a limit as x -> r then you get the right answer

    what you should do is do the integral in polar coordinates
  4. Dec 30, 2009 #3
    Thank you!

    Setting my calculator to use rad (was set on deg) and using limits made it work.
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