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Let f(x) = 2 - |x - 1| and g(x) = (x - 1)². Identify the correct statement(s) about the regions bounded by these curves.

1. (A) The area bounded by f(x) and g(x) is 7/6
2. (B) The area bounded by f(x) and g(x) is 7/3
3. (C) The area bounded by f(x), g(x) and the x-axis is 5/3
4. (D) The area bounded by f(x), g(x) and the x-axis is 5/6

Correct answer: (B) The area bounded by f(x) and g(x) is 7/3

Solution

With u = x - 1 the curves meet at u = +/-1, and the symmetric area between f and g evaluates to 7/3, so (B) is correct.

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