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Homework Help: Finding the area of a circle using integration

  1. May 7, 2010 #1
    Let's say I have the equation for a circle but don't know how to calculate its radius. How could I use integration to find its area?
     
  2. jcsd
  3. May 7, 2010 #2
    You can always get the radius from circle equations !!

    However, all circle equations are integrated by trigonometric substitution
    and it can also be done by integration by parts but that is a bit tricky!!
     
  4. May 7, 2010 #3

    jack action

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    Gold Member

    The area of a circle is a equal to the area of two half-circle.

    The equation of a half-circle (assuming (y-b) is always positive and that you don't understand that r is the radius):

    [tex]\left(x-a\right)^2+\left(y-b\right)^2=r^2[/tex]

    So the area of a circle is equal to: [tex]2\int_{-r-a}^{r-a}y_{(x)}dx[/tex]

    That's a complicated way, but I guess it can be done.
     
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