0
$\begingroup$

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?

$\endgroup$
1
$\begingroup$

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

$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.