Answer: 14/3.
- A 14/3
- B 10/3
- C 16/3
- D 4
Correct answer: A. 14/3
Explanation: Area = integral 0 to 2 of (x<sup>2</sup>+1) dx = [x<sup>3</sup>/3 + x] from 0 to 2 = 8/3 + 2 = 14/3.
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.