QJEEM23Ma79dc: JEE Main 2023 Mathematics - Class 12 JEEM23Ma79dc Solution: The area of the region enclosed by the curve and the -axis is

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

Accepted Answer

Area =

=

\begin{aligned}&amp;\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}&amp; =\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| \\\\&amp; = 2+\frac{2}{\sqrt{2}}+2-\frac{2}{\sqrt{2}}=4\end{aligned}

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