> 
> Compute $$\int\_C x\sqrt{x^2-y^2} \mathrm ds$$ 
>  where $C:(x^2+y^2)^2=a^2(x^2-y^2)$ with $x\geq 0$.
> 
> 
> 

My attempt: 

For this I tried the parametrization: $x=r\cos t,y=r\sin t$, but it doesn't seem to work and I get to: $\cos(2t)=\dfrac 1{a^2}$, so $t\in \left[3\dfrac {\pi}2,5\dfrac {\pi}2 \right]$?