Question

If the area bounded by the curves
$y=|{\cos }^{-1}\left(\sin x\right)|+|\frac{\pi }{2}-({\cos }^{-1}\cos x\left)\right|,x$- axis and $\frac{\pi }{2}<x<\pi$ is equal to $\frac{{\pi }^2}{k}$ , then $k$ is -

• A. $12$
• B. $8$
• C. $4$
• D. $1$

Answer 1

The correct option is C $4$

$y=|\frac{\pi }{2}-(\pi -x\left)\right|+|\frac{\pi }{2}-x|=2x-\pi \forall x\in [\frac{\pi }{2},x]$


$\text{Area}=\frac{1}{2}\times \frac{\pi }{2}\times \pi =\frac{{\pi }^2}{4}$