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:

Accepted Answer

The required area is shown by shaded region

$$A = \int\limits_1^3 {\left| {x - 2} \right|dx = 2\int\limits_2^3 {\left( {x - 2} \right)} } dx$$

$$ = 2\left[ {{{{x^2}} \over 2} - 2x} \right]_2^3 = 1$$

Solutions · 1