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)

$2\sqrt{2}-2$

Answer 2

$y = | cos\, x - sin\, x |$
Required area $\int\limits^{\pi/4}_{{0}}(cos\, x -sin \,x) \,dx$
$=2\left[sin\,x+cos\,x\right]^{\pi/4}_{0}=2\left[\frac{2}{\sqrt{2}}-1\right]$
$=\left(2\sqrt{2}-2\right)$ s units