Answer: pi a2.
- A pi a
- B 2 pi a
- C pi a2
- D 4a2
Correct answer: C. pi a2
Explanation: Using integration (4 times the first-quadrant area), the area of the circle x2+y2=a2 comes out to pi a2, 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.