Answer: 2.
- A 2
- B 0
- C π
- D 1
Correct answer: A. 2
Explanation: ∫sin x dx = −cos x; from 0 to π gives (−cos π) − (−cos 0) = 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.