Question

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 = p/4 and x = b, $\left( \beta > \frac{\pi}{4} \right)$ is b sin b + $\frac{\pi}{4}$cosb + $\sqrt{2}$b + 130, 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. $\left( 1 - \frac{\pi}{4} + \sqrt{2} \right)$

Answer 1

Answer: (D)

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

Answer 2

Newton – Leibnitz based