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

Question

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

Accepted Answer

Given equation of curve $y=|x-1|+|x-2|$ and $y=3$

When, $x-1=0 \Rightarrow x=1$, then $y=1$

and when, $x-2=0 \Rightarrow x=2$, then $y=1$

Equation of curve passing through point $(1,1)$ and $(2,1)$ and $(0,3),(3,3)$

$\therefore$ Area bounded by given curves

$$
=\frac{1}{2}(1+3) \times 2(\text { Area of trapezium })=4
$$

Solutions · 1