Answer: pi a 2.
- A pi a
- B 2 pi a
- C pi a<sup>2</sup>
- D 4a<sup>2</sup>
Correct answer: C. pi a<sup>2</sup>
Explanation: Using integration (4 times the first-quadrant area), the area of the circle x<sup>2</sup>+y<sup>2</sup>=a<sup>2</sup> comes out to pi a<sup>2</sup>, matching the known formula.
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.