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