The area under the curve y=| x- x|, 0 x2, and above the x-axis is:

Question

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

Accepted Answer

$$\text{Area} = 2\int_0^{\pi/4}(\cos x-\sin x)\,dx = 2[\sin x+\cos x]_0^{\pi/4} = 2\left(\sqrt2-1\right) = 2\sqrt2-2$$

Solutions · 1