Answer: πr².
- A πr²
- B 2πr
- C πr
- D r²
Correct answer: A. πr²
Explanation: Integrating the circle’s equation gives the enclosed area πr².
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.