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

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Solution

The correct option is A 1
Area = $\int_{1}^{3} | x - 2 | d x = \int_{1}^{2} (2 - x) d x + \int_{1}^{3} (x - 2) d x = {[2 x - \frac{x^{2}}{2}]}_{1}^{2} + {[\frac{x^{2}}{2} - 2 x]}_{2}^{3}$
$= (4 - 2) - (2 - \frac{1}{2}) + (\frac{9}{2} - 6) - (2 - 4) = \frac{1}{2} + \frac{1}{2} = 1$

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