question_answer

The area enclosed between  \[f(x)=Min\,\,({{\cos }^{-1}}(\cos x),\,co{{t}^{-1}}(\cos x))\] and x-axis in \[x\in (\pi ,2\pi )\] is

A) \[{{\pi }^{2}}/4\]

B)                    \[{{\pi }^{2}}/3\]                

C) \[{{\pi }^{2}}/2\]                 

D)        \[{{\pi }^{2}}\]

Correct Answer: A

Solution :

[a] Clearly, required area = Area of shaded part \[=\frac{1}{2}\times \pi \times \frac{\pi }{2}=\frac{{{\pi }^{2}}}{4}\]