Curve is given by equation:
$$r^2 = 2a^2|\cos \phi|$$
I would like to use the formula: $$A = \frac{1}{2}\int_a^b (f(\phi))^2 \, d\phi$$
So, since equation is already squared, i can put the right side of it directly into formula. Also, because there is absolute value of $\cos \phi$, the equation is correct for every $\phi$ in $[0;2\pi]$. So it comes to:
$$A = \frac{1}{2}\int_{0}^{2\pi}2a^2|\cos \phi| \, d \phi$$
$$A = a^2\int_0^{2\pi} |\cos \phi| \, d \phi = 4a^2$$
Question is: is my way of solution correct? It seems to be too simple, and I have feeling like I didn't notice something. Thanks for any answers.