The area of the region bounded by the curves y = | x - 2 | , x = 1 , x = 3 and the X -axis is:

Question

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

Smart Achievers · Accepted Answer

(4)

Ans. 1 sq. unit

Explanation:

Required area, $A = \int_{1}^{3}$ $| x - 2 |$ $d x$

$= \int_{1}^{2} (2 - x) d x + \int_{2}^{3} (x - 2) d x$

$= {[2 x - \frac{x^{2}}{2}]}_{1}^{2} + {[\frac{x^{2}}{2} - 2 x]}_{2}^{3}$

$= \frac{1}{2} + \frac{1}{2} = 1 sq. unit.$

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