Answer: πa².
- A πa²
- B 2πa
- C πa
- D a²
Correct answer: A. πa²
Explanation: The enclosed area of a circle of radius a is πa².
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.