The area of the region bounded by the curve y | vedclass

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(A) The given curve is $y = |x - 2|$.We need to find the area bounded by $y = |x - 2|$,$x = 1$,$x = 3$,and the $X$-axis.The function $y = |x - 2|$ can

Vedclass · Accepted Answer

$1 	ext{ sq.units}$

Vedclass · Answer

(A) The given curve is $y = |x - 2|$.We need to find the area bounded by $y = |x - 2|$,$x = 1$,$x = 3$,and the $X$-axis.The function $y = |x - 2|$ can be defined as:$y = \begin{cases} -(x - 2) & 	ext{if } x The area $A$ is given by the integral:$A = \int_{1}^{3} |x - 2| \, dx$Splitting the integral at $x = 2$:$A = \int_{1}^{2} -(x - 2) \, dx + \int_{2}^{3} (x - 2) \, dx$$A = \left[ -\frac{(x - 2)^2}{2} ight]_{1}^{2} + \left[ \frac{(x - 2)^2}{2} ight]_{2}^{3}$$A = \left( 0 - (-\frac{(1 - 2)^2}{2}) ight) + \left( \frac{(3 - 2)^2}{2} - 0 ight)$$A = \frac{1}{2} + \frac{1}{2} = 1 	ext{ sq.units}$.

The area of the region bounded by the curve $y=|x-2|$ between $x=1, x=3$ and the $X$-axis is ......

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