Answer: ln 2.
- A ln 2
- B ln 1
- C 1
- D 2
Correct answer: A. ln 2
Explanation: ∫(1/x) dx = ln|x|; from 1 to 2 gives ln 2 − ln 1 = ln 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.