MCQ
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 $x=\beta>\frac{\pi}{4}$ is $\left(\beta \sin \beta+\frac{\pi}{4} \cos \beta+\sqrt{2} \beta\right)$. Then $f\left(\frac{\pi}{2}\right)$ is
- ✓$1-\frac{\pi}{4}+\sqrt{2}$
- B$1-\frac{\pi}{4}-\sqrt{2}$
- C$\frac{\pi}{4}-\sqrt{2}+1$
- D$\frac{\pi}{4}+\sqrt{2}-1$