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Find the area of the region bounded by the curves f(x) = (x - 4)² and g(x) = 16 - x² together with the x-axis.

1. 64/3
2. 128/3
3. 32
4. 16

Correct answer: 64/3

Solution

Both parabolas meet at (0,16) and both reach the x-axis at x=4; the area enclosed with the x-axis from x=0 to 4 is the integral of (16 - x²) minus (x-4)², giving 64/3.

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