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The area of the shaded region between two curves y = f(x) and y = g(x) over [a, b] is correctly given by which of the following?
- integral a to b of |f(x) - g(x)| dx
- integral a to b of (|f(x)| - |g(x)|) dx
- integral a to b of (|f(x)| + |g(x)|) dx
- integral a to b of |f(x) + g(x)| dx
Correct answer: integral a to b of |f(x) - g(x)| dx
Solution
Area between two curves is the integral of the vertical gap, i.e. |f(x) - g(x)|, taken over the interval.
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