Answer: 1.
- A 1
- B e - 1
- C ln(e) = 1
- D e
Correct answer: A. 1
Explanation: Area = integral from 1 to e of (1/x) dx = [ln x] from 1 to e = ln(e) - ln(1) = 1 - 0 = 1.
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.