Answer: 2.
- A 0
- B 1
- C 2
- D pi
Correct answer: C. 2
Explanation: Area = integral from 0 to pi of sin x dx = [-cos x] from 0 to pi = -cos(pi) - (-cos(0)) = 1 + 1 = 2 (sin x is non-negative on [0,pi], so the integral directly gives area).
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.