The area of the region enclosed by the curve f(x)=max x, x,- x and the x-axis is

Question

The area of the region enclosed by the curve
$f(x)=max{\sin x,\cos x},-\pi \le x\le \pi $ and the $x$-axis is

Accepted Answer

Area =

= $$
\begin{aligned}
&\left|\int_{-\pi}^{-3 \pi / 4} \sin x d x\right|+\left|\int_{\pi / 4}^\pi \sin x d x\right|+\left|\int_{-3 \pi / 4}^{-\pi / 2} \cos x d x\right|
+\left|\int_{-\pi / 2}^{\pi / 4} \cos x d x\right|
\end{aligned}
$$

$$
\begin{aligned}
& =\left|\frac{1}{\sqrt{2}}-1\right|+\left|1+\frac{1}{\sqrt{2}}\right|+\left|-1+\frac{1}{\sqrt{2}}\right|+\left|\frac{1}{\sqrt{2}}+1\right| \\
& = 2+\frac{2}{\sqrt{2}}+2-\frac{2}{\sqrt{2}}=4
\end{aligned}
$$

Solutions · 1