<p>Area bounded by \(y=|x-1|\) and \(y=1\). [JEE Main 2014]</p>
Step-by-Step Solution
Key Concept: |x-1|\leq1 for x\in [0,2]. Area = \int_0^2(1-|x-1|)dx = 2\int_0^1(1-(1-x))dx = 2 \cdot (1/2) = 1.
<div class='solution'>
<p>Intersections: $|x-1|=1\Rightarrow x=0,2$. On $[0,2]$: $y=1\ge|x-1|$.</p>
<p>$$A=\int_0^2(1-|x-1|)dx=2\int_0^1 x\,dx=2\cdot\frac{1}{2}=1$$</p>
</div>
Correct Answer: A