Question

The area under the curve $y=|\cos x-\sin x|,0\le x\le \frac{\pi }{2},$ and above x-axis is :

• A. $2\sqrt{2}$
• B. $2\sqrt{2}-2$
• C. $2\sqrt{2}+2$
• D. 0

Answer 1

Answer: (B)

$y=|\cos x-\sin x|$

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