The area bounded by the curve $y=|x-2|, x=1$, $x=3$ and $\mathrm{X}$-axis is

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Aicharya · Accepted Answer

$\begin{aligned} 	ext { Required area } & =\int_1^3|x-2| \mathrm{d} x \ & =\int_1^2(2-x) \mathrm{d} x+\int_2^3(x-2) \mathrm{d} x \ & =\left[2 x-\frac{x^2}{2}ight]_1^2+\left[\frac{x^2}{2}-2 xight]_2^3 \ & =\frac{1}{2}+\frac{1}{2}=1 	ext { sq. unit }\end{aligned}$

The area bounded by the curve $y=|x-2|, x=1$, $x=3$ and $\mathrm{X}$-axis is

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