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

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

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.

2. ## 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

$\displaystyle \frac{1}{2}\int_0^{\infty } x^2 \, dt$

3. ## Re: Help with Area of a Lemniscate Using Green's theorem

Originally Posted by Idea
$\displaystyle y=x t$

$\displaystyle dy=x dt+t dx$

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

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.

4. ## Re: Help with Area of a Lemniscate Using Green's theorem

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