Answer: Non-negative quantity.
- A Negative quantity
- B Non-negative quantity
- C Complex number
- D Function of x only, never a number
Correct answer: B. Non-negative quantity
Explanation: Even though a definite integral can be negative, the area itself is defined as a non-negative quantity, so absolute values are taken where needed.
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.