The area bounded by the curve $y=\cos x$, the line joining $(-\pi / 4, \cos (-\pi / 4))$ and $(0,2)$ and the line joining $(\pi /$ $4, \cos (\pi / 4))$ and $(0,2)$ is

• Correct answer
  A

  $\left(\frac{4+\sqrt{2}}{8}\right) \pi-\sqrt{2}$
• B

  $\left(\frac{4+\sqrt{2}}{8}\right) \pi+\sqrt{2}$
• C

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

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

Solution

required area $=2\left[\frac{1}{2}\left(\frac{1}{\sqrt{2}}+2\right) \frac{\pi}{4}-\int_{0}^{\pi / 4} \cos x \mathrm{dx}\right]$ $=\left(\frac{4+\sqrt{2}}{8}\right) \pi-\sqrt{2}$

Hence, the correct answer is option: 'A'.