Answer: 9 pi/4.
- A 9 pi/4
- B 9 pi/2
- C 3 pi
- D 9 pi
Correct answer: A. 9 pi/4
Explanation: Total circle area = pi(3)<sup>2</sup> = 9pi. The first quadrant is one-fourth of the circle: 9pi/4.
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.