Answer: 8/3.
- A 8/3
- B 4
- C 4/3
- D 2
Correct answer: A. 8/3
Explanation: ∫x² dx = x³/3; from 0 to 2 gives 8/3.
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.