Answer: Integral from a to b of f(x) dx.
- A f(b) - f(a)
- B Integral from a to b of f(x) dx
- C f(a) + f(b)
- D Derivative of f at b minus derivative at a
Correct answer: B. Integral from a to b of f(x) dx
Explanation: The area bounded by a non-negative curve, the x-axis, and the vertical lines x=a, x=b is the definite integral from a to b of f(x) dx.
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.