Answer: 1/2.
- A 1/2
- B 0
- C 1
- D 1/4
Correct answer: A. 1/2
Explanation: Each half contributes 1/4, so the total (unsigned) area is 1/2.
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.