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

A

$$\left(\frac{\pi}{4} + \sqrt{2} - 1\right)$$

B

$$\left(\frac{\pi}{4} - \sqrt{2} + 1\right)$$

C

$$\left(1 - \frac{\pi}{4} - \sqrt{2}\right)$$

D

$$\left(1 - \frac{\pi}{4} + \sqrt{2}\right)$$