Answer: 9.
- A 3
- B 6
- C 9
- D 27
Correct answer: C. 9
Explanation: Area = integral from 0 to 3 of x<sup>2</sup> dx = [x<sup>3</sup>/3] from 0 to 3 = 27/3 - 0 = 9.
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.