Answer: πab.
- A πab
- B πa²
- C πb²
- D 2πab
Correct answer: A. πab
Explanation: The area of an ellipse is πab, reducing to πr² when a = b = r.
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.