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  1. #1
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    Question double integral

    Use a double integral in polar coordinates to find the area of the region inside the circle x^2 + y^2 =4 and to the right of the line x=1.

    Thank you very much.
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  2. #2
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    I still don't know how to solve this question. If you can help, please do. Thank you very much.
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  3. #3
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    Hello, kittycat!

    Use a double integral in polar coordinates to find the area of the region
    inside the circle x^2 + y^2 \:=\:4 and to the right of the line x=1.
    Code:
                    |Y
                    |
                  * * *   |
              *     |     *P
            *       |     |:*
           *        |     |::*
                    |     |:::
          *         |     |:::*
      - - * - - - - + - - +:-:* - -
          *         |O   1|:::*2  X
                    |     |:::
           *        |     |::*
            *       |     |:*
              *     |     *Q
                  * * *   |
                    |

    The polar equation of the circle is: . r \,=\,2
    The polar equation of x = 1 is: . r \,=\,\sec\theta

    Draw radii OP and OQ.
    We find that: . P(1,\,\sqrt{3}),\;Q(1,\,\text{-}\sqrt{3})
    . . and that: \angle POX \,=\,\angle QOX \,=\,\frac{\pi}{3}

    The double integral is: . A \;=\;\int^{\frac{\pi}{3}}_{\text{-}\frac{\pi}{3}} \int^2_{\sec\theta} r\,dr\,d\theta

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  4. #4
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    okay , i got it now. Many thanks )
    Last edited by kittycat; August 3rd 2007 at 09:50 AM.
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  5. #5
    Eater of Worlds
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    Hey Kittycat:

    Just for fun (yes, we mathnerds think it's fun), here it is in rectangular coordinates.

    2\int_{1}^{2}\int_{0}^{\sqrt{4-x^{2}}}dydx
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