Here is my task:
Calculate area of region $(x^{2}+y^{2})^{2}\leq a^{2}(x^{2}-y^{2})$.
Here is what I have done. After transforming this line to polar form $(x=\rho\cos\phi,y=\rho\sin\phi)$, we have:
$\rho=a\sqrt{\cos 2\phi}$
This line looks like:
http://postimg.org/image/x9pmfqrn1/
So area would be $P=4P1$, where $P1=\int_{0}^{\frac{\pi}{2}}d\phi\int_{0}^{a\sqrt{\cos2\phi}} \rho d\rho$,but I got P1=0. Why?