Answer: 2.
- A 2
- B 1
- C π
- D 0
Correct answer: A. 2
Explanation: ∫₀^π sin x dx = 2, the area of one full arch.
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.