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Given f(x) = 2 - |x - 1| and g(x) = (x - 1)², find the area of the region bounded by the curves y = f(x) and y = g(x).

1. 7/6
2. 7/3
3. 7/2
4. 7/4

Correct answer: 7/3

Solution

The curves intersect at x = 0 and x = 2. Splitting at x = 1, each piece contributes 7/6, giving a total bounded area of 7/3.

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