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Math Help - find area of ellipse by green theorem

  1. #1
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    find area of ellipse by green theorem

    1. By greens theorem, find an expression for the area of the region R, and apply this to evaluate the area of the ellipse bounded by the curve.

    x= a cos theta, y=b sin theta
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  2. #2
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    Quote Originally Posted by szpengchao View Post
    1. By greens theorem, find an expression for the area of the region R, and apply this to evaluate the area of the ellipse bounded by the curve.

    x= a cos theta, y=b sin theta
    Parametrize the curve as \bold{g}(\theta) = (g_1(\theta),g_2(\theta)) for 0\leq \theta \leq 2\pi where g_1(\theta)=a\cos \theta and g_2(\theta) = b\sin \theta.

    Then, \iint_R 1 dA=\frac{1}{2}\int_C -ydx + xdy.

    Now evaluate that line integral to get the answer.
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