The area of the bounded region enclosed by the curve y=3- |x-(1)/(2) |-|x+1| and the x -axis is :

Application of Integrals: The area of the bounded region enclosed by the curve y=3- |x-(1)/(2)… | JEE Main 2022

JEE Main 2022 (Online) 28th June Evening ShiftQuestion 1

The area of the bounded region enclosed by the curve $y=3-\left|x-\frac{1}{2}\right|-|x+1|$ and the $x$-axis is :

Application of Integrals

$\frac{9}{4}$$\frac{45}{16}$$\frac{27}{8}$✓ Correct answer$\frac{63}{16}$

Solution

Breakpoints $x=-1,\frac12$. For $x\le-1$: $y=2x+\frac72$ (zero at $x=-\frac74$). For $-1\le x\le\frac12$: $y=\frac32$. For $x\ge\frac12$: $y=\frac52-2x$ (zero at $x=\frac54$). Area $=\frac12\cdot\frac34\cdot\frac32+\frac32\cdot\frac32+\frac12\cdot\frac34\cdot\frac32=\frac9{16}+\frac94+\frac9{16}=\frac{27}8$. Option (C).

Application of Integrals - JEE Mathematics question (JEE Main 2022 (Online) 28th June Evening Shift)

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