Mathematics - Area Under Curves Question with Solution | TestHub

Writing $x=\frac{a^3}{y^2+a^2}$, the asymptote is $x=0$. Required area $=2{\int }_0^{\infty }\frac{a^3}{y^2+a^2}dy=2a^3\cdot \frac{1}{a}{\left[{\tan }^{-1}\frac{y}{a}\right]}_0^{\infty }=$ $\underline{2a^2}\cdot \frac{\pi }{2}=\pi a^2$.