Area of the bounded region between the curve $y = |x-2|$ and the line $y = 2$ is:
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → 4 square units
$\text{Intersections: }|x-2|=2\;\Rightarrow\;x=0,4.$
$\text{Area }=\displaystyle\int_{0}^{2}\big[2-(2-x)\big]\,dx+\int_{2}^{4}\big[2-(x-2)\big]\,dx =\int_{0}^{2}x\,dx+\int_{2}^{4}(4-x)\,dx$
$=\left[\frac{x^{2}}{2}\right]_{0}^{2}+\left[4x-\frac{x^{2}}{2}\right]_{2}^{4}=2+2=4.$