Answer: Integral of [f(x) - g(x)] dx from a to b.
- A Integral of f(x) dx alone, without subtracting g(x)
- B Integral of [f(x) - g(x)] dx from a to b
- C Integral of [f(x) + g(x)] dx from a to b
- D f(b) minus g(a), the difference of two endpoint values
Correct answer: B. Integral of [f(x) - g(x)] dx from a to b
Explanation: Area between two curves is the integral of (upper curve minus lower curve) over the interval.
The definite integral ∫ₐᵇf(x)dx computes the exact area of the shaded region bounded by the curve, the x-axis, and the vertical lines x=a and x=b - the same idea behind the Riemann sum, but evaluated exactly rather than approximated by rectangles.
Concept context
Using definite integrals to compute the area under a curve, the area between two curves, and the areas enclosed by standard curves like circles, parabolas, and ellipses.