Mathematics - Area Under Curves Question with Solution | TestHub

Let $\alpha ,\beta$ be the roots of $18x^2-9\pi x+{\pi }^2=0$, where $\alpha <\beta$. Also $f(x)=x^2$ and $g(x)=\cos x$. If the area bounded by $y=(f\circ g)(x)$, the lines $x=\alpha ,x=\beta$ and the $x$-axis is $\frac{\pi }{\lambda }$, find the sum of the digits of $\lambda$.