Answer: (pi r2)/2.
- A pi r2
- B (pi r2)/2
- C 2 pi r
- D pi r
Correct answer: B. (pi r2)/2
Explanation: A semicircle is half of a full circle, so its area is (pi r2)/2.
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.