Answer: a strictly non-negative value.
- A a strictly non-negative value
- B a strictly negative value
- C an always-zero value
- D a possibly complex value
Correct answer: A. a strictly non-negative value
Explanation: Area is measured as a non-negative amount, so we use absolute values where a curve dips below the axis.
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.