Answer: pi a b.
- A pi a b
- B pi(a+b)
- C pi a<sup>2</sup> b<sup>2</sup>
- D 2 pi a b
Correct answer: A. pi a b
Explanation: By integration over the ellipse (4 times the first-quadrant area), the total enclosed area is pi a b.
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.