<p>The area enclosed by \(y=1-|1-x|\) and \(y=0\) over \([0,2]\) is: [MAU051]</p>
Step-by-Step Solution
Key Concept: y=1-|1-x| forms a triangle with peak at (1,1). Base from x=0 to x=2. Area = (1/2) \cdot 2 \cdot 1 = 1.
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<p>On $[0,1]$: $|1-x|=1-x$, so $y=1-(1-x)=x$.</p>
<p>On $[1,2]$: $|1-x|=x-1$, so $y=1-(x-1)=2-x$.</p>
<p>This is a triangle with vertices $(0,0),(1,1),(2,0)$. Area $=\frac{1}{2}\cdot2\cdot1=\boxed{1}$.</p>
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Correct Answer: ['A']