Let $f:\left[0, \frac{\pi}{2}\right] \rightarrow[0,1]$ be the function defined by $f(x)=\sin ^2 x$ and let $g:\left[0, \frac{\pi}{2}\right] \rightarrow[0, \infty)$ be the function defined by $g(x)=\sqrt{\frac{\pi x}{2}-x^2}$. (There are two questions based on PARAGRAPH "II", the question given below is one of them)

The value of $2 \int_0^{\frac{\pi}{2}} f(x) g(x) d x-\int_0^{\frac{\pi}{2}} g(x) d x$ is