Answer: 2.
- A 1
- B 2
- C π
- D π/2
Correct answer: B. 2
Explanation: ∫₀^π sinx dx = [−cosx]₀^π = 1 + 1 = 2.
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.