Area of region - double integral

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?

$$P1=\int_{0}^{\color{red}{\frac{\pi}{4}}}d\phi\int_{0}^{a\sqrt{\cos2\phi}} \rho d\rho.$$ (Note $\cos2\phi=0$ when $\phi=\pi/4$.)