Question

The area of the region bounded by Y-axis, $y=\cos x$ and $y=\sin x$ , $0\le x\le \frac{\pi }{2}$ is

• A. $\sqrt{2}+1$ square units
• B. $\sqrt{2}-1$ square units
• C. $2-\sqrt{2}$ square units
• D. $\sqrt{2}$ square units

Answer 1

The correct option is B $\sqrt{2}-1$ square units



Required area $=\underset{0}{\overset{\pi /4}{\int }}(\cos x-\sin x)dx$
$=[\sin x+\cos x{]}_0^{\pi /4}$
$=\sqrt{2}-1$