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Two curves y = f(x) and y = g(x) meet at (0,4), (2,2) and (4,0), with f(x) > g(x) for 0 < x < 2 and f(x) < g(x) for 2 < x < 4. If integral from 0 to 4 of |f(x) - g(x)| dx = 10 and integral from 2 to 4 of |g(x) - f(x)| dx = 5, then the area between the curves over 0 < x < 2 is:

1. 5
2. 10
3. 15
4. 20

Correct answer: 5

Solution

Since the absolute area over [0,4] is 10 and over [2,4] is 5, the area over [0,2] is 10 - 5 = 5.

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