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If f(x) and g(x) are continuous functions over the interval a ≤ x ≤ b, and p(x) represents the greater of f(x) and g(x), while q(x) represents the lesser of f(x) and g(x), what is the expression for the area enclosed by the curves y = p(x), y = q(x), and the vertical lines x = a and x = b?

1. ∫[a to b] (f(x) - g(x)) dx
2. ∫[a to b] (p(x) - q(x)) dx
3. ∫[a to b] |p(x) - q(x)| dx
4. ∫[a to b] |f(x) - g(x)| dx

Correct answer: ∫[a to b] (p(x) - q(x)) dx

Solution

The expression for the area enclosed by the curves y = p(x), y = q(x), and the vertical lines x = a and x = b is ∫[a to b] (p(x) - q(x)) dx because it represents the difference between the greater and lesser functions over the interval.

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