Answer: The absolute value of the definite integral (which is negative).
- A Equal to the definite integral, treating it as positive
- B The absolute value of the definite integral (which is negative)
- C Zero in this particular case, regardless of the curve's shape
- D Equal to b minus a, the width of the interval alone
Correct answer: B. The absolute value of the definite integral (which is negative)
Explanation: When f(x) < 0 on [a,b], the definite integral is negative; the actual area is its absolute value.
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.