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