Answer: 6π.
- A 6π
- B 12π
- C 36π
- D 5π
Correct answer: A. 6π
Explanation: Area = πab = π·3·2 = 6π.
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.