Answer: 16/3.
- A 8
- B 16/3
- C 32/3
- D 4
Correct answer: B. 16/3
Explanation: The curve meets the x-axis at x=2. Area = integral from 0 to 2 of (4-x<sup>2</sup>) dx = [4x - x<sup>3</sup>/3] from 0 to 2 = 8 - 8/3 = 16/3.
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.