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Thread: Help with Area of a Lemniscate Using Green's theorem

  1. #1
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    Help with Area of a Lemniscate Using Green's theorem

    Help with Area of a Lemniscate Using Green's theorem-capture.png

    The only problem I cannot seem to get the answer to for my homework . I have 2 tries left, and I can't seem to figure out what is the solution. Can someone help me out ? I've spent so long on this problem.
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    Re: Help with Area of a Lemniscate Using Green's theorem

    $\displaystyle y=x t$

    $\displaystyle dy=x dt+t dx$

    $\displaystyle x dy - y dx = x^2 dt$

    so the area is given by

    $\displaystyle \frac{1}{2}\int_0^{\infty } x^2 \, dt$
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  3. #3
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    Re: Help with Area of a Lemniscate Using Green's theorem

    Quote Originally Posted by Idea View Post
    $\displaystyle y=x t$

    $\displaystyle dy=x dt+t dx$

    $\displaystyle x dy - y dx = x^2 dt$

    so the area is given by

    $\displaystyle \frac{1}{2}\int_0^{\infty } x^2 \, dt$
    that can't be correct. The integral doesn't converge.
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    Re: Help with Area of a Lemniscate Using Green's theorem

    Quote Originally Posted by romsek View Post
    that can't be correct. The integral doesn't converge.
    $x$ is a function of $t$
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