Answer: 12.
- A 3
- B 12
- C 15
- D 8
Correct answer: B. 12
Explanation: Area = integral from 1 to 5 of 3 dx = 3(5-1) = 12, which is just the rectangle area.
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.