The area bounded by the curves y = x - 1 + x - 2 and y = 3 is equal to

Given:

$y=f\left(x\right)=\left|x-1\right|+\left|x-2\right|$

$$\begin{gathered} \Rightarrow f\left(x\right)=\left\{\begin{array}{l}3-2x: x<1 \\ 1; 1\le x<2\\ 2x-3; x\ge 2\end{array}\right. \end{gathered}$$

Let us draw diagram of $y=f\left(x\right) \& y=3$ we get,

Required area is the area of trapezium which is

Area $=\frac{1}{2}\left[1+3\right]\times 2$

$=4$ sq. units