integrate f(x,y)=1/((1+x^2+y^2))^2 over the region enclosed by one loop of the leminisciate r^2=cos2(theta)

here i know it has to be converted into polar coordinates

what would be the limits

as i dont know the grapho of r^2=cos2(theta)

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- Dec 1st 2012, 01:10 AMprasumpolar integration 1
integrate f(x,y)=1/((1+x^2+y^2))^2 over the region enclosed by one loop of the leminisciate r^2=cos2(theta)

here i know it has to be converted into polar coordinates

what would be the limits

as i dont know the grapho of r^2=cos2(theta) - Dec 3rd 2012, 08:21 AMhollywoodRe: polar integration 1
The graph of your lemniscate looks like the symbol for infinity.

The equation has no solutions where $\displaystyle \cos{2\theta}$ is negative; the two loops are formed from the two intervals where $\displaystyle \cos{2\theta}$ is positive.

- Hollywood