The area bounded by the curves $y=|x-1|+|x-2|$ and $y=3$ is equal to
Step-by-Step Solution
Key Concept: $f(x)=|x-1|+|x-2|$ simplifies to $3-2x$ for $x<1$, $1$ for $1\leq x<2$, $2x-3$ for $x\geq 2$. The region between $f(x)$ and $y=3$ forms a trapezium.
Trapezium with parallel sides $3-1=2$ (at $y=1$, width $=0$ since the plateau has width $1$) and width $3$ at $y=3$. More precisely, area $=\frac{1}{2}(1+3)\times 2=4$.
Correct Answer: 1