Question

$Letf\left(x\right)={sin}^{-1}\left(sinx\right)+{cos}^{-1}\left(cosx\right),g\left(x\right)=mxandh\left(x\right)=x$ are three functions. Now g(x) is divided area between f(x),x=$\pi$ and y=0 into two equal parts.
The area bounded by the curve y=f(x), x=$\pi$ and y=0 is:

• A. $\frac{{\pi }^2}{4}sq.units$
• B. ${\pi }^{2}sq.units$
• C. $\frac{{\pi }^2}{8}sq.units$
• D. $2{\pi }^{2}sq.units$

Answer 1

The correct option is B ${\pi }^{2}sq.units$

Given,

$f\left(x\right)={\sin }^{-1}\sin x+{\cos }^{-1}\cos x=x+x=2x$

$x=\pi$

$y=0$

The above 3 forms a right angled triagle, with center as one vertex.

$Area=\frac{1}{2}\times \pi times2\pi$

$={\pi }^{2}sq.units$