Answer: 9.
- A 9
- B 27
- C 3
- D 18
Correct answer: A. 9
Explanation: ∫x² dx = x³/3; evaluated from 0 to 3 gives 27/3 = 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.