Answer: (8/3)a².
- A (8/3)a²
- B (4/3)a²
- C 2a²
- D a²
Correct answer: A. (8/3)a²
Explanation: This standard result gives the enclosed area as 8a²/3.
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.