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Let f(x) = 2 - |x - 1| and g(x) = (x - 1)². Which of the following is correct?

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

Correct answer: The area enclosed between f(x) and g(x) is 7/3

Solution

With t = x-1, the upper curve is 2 - |t| and lower is t² between their intersections t = -1 and t = 1; the enclosed area evaluates to 7/3.

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