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Math Help - prove area of ellipse

  1. #1
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    Question prove area of ellipse

    Show that the area of ellipse

    x^2/a^2 + y^2/b^2 =1 is pi*ab.
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  2. #2
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    It's symmetric with respect to the y axis.

    We consider to compute the half area of the ellipse, then when you get the final answer, multiply by 2 and you are done.

    It remains to compute \int_{-a}^a\sqrt{b^2\left(1-\frac{x^2}{a^2}\right)}\,dx
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