Let $f(x)$ be a non-negative continuous function such that the area bounded by the curve $y=f(x)$, $x-axis$ and the ordinates $x=\frac{\pi}{4}$ and $x=\beta > \pi/4$ is <br> $( \beta \sin \beta + \frac{\pi}{4} \cos \beta + \sqrt{2} \beta)$. Then $f(\frac{\pi}{2})$ is :

Question

( A ) $(1 - \frac{\pi}{4} - \sqrt{2})$
( B ) $(\frac{\pi}{4} + \sqrt{2} - 1)$
( C ) $(\frac{\pi}{4} - \sqrt{2}+1)$
( D ) $(1 - \frac{\pi}{4} + \sqrt{2})$