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

Question

Aicharya · Accepted Answer

$ 	ext { } y=|\cos x-\sin x| $ $ \begin{aligned} 	ext { Required area } & =2 \int_0^{\pi / 4}(\cos x-\sin x) d x \ & =2\left[\sin x+\cos x 0_0^{\pi / 4}ight] \ & =2\left[\frac{2}{\sqrt{2}}-1ight]=(2 \sqrt{2}-2) 	ext { sq. units } \end{aligned} $

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

Solution