JEE Main 2023 (Online) 13th April Morning ShiftQuestion 1
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
Application of Integrals
Solution
$\max(\sin x,\cos x)$: $\sin x$ on $[-\pi,-\tfrac{3\pi}4]\cup[\tfrac\pi4,\pi]$, $\cos x$ on $[-\tfrac{3\pi}4,\tfrac\pi4]$. Area $=\int|f|$: $\int_{-\pi}^{-3\pi/4}|\sin x|=1-\tfrac{\sqrt2}2$; $\int_{-3\pi/4}^{-\pi/2}|\cos x|=1-\tfrac{\sqrt2}2$; $\int_{-\pi/2}^{\pi/4}\cos x=1+\tfrac{\sqrt2}2$; $\int_{\pi/4}^{\pi}\sin x=1+\tfrac{\sqrt2}2$. Total $=4$. Answer: (B).