Answer: -1.
- A -1
- B 1
- C 0
- D undefined
Correct answer: A. -1
Explanation: Integration by parts: u=ln x, dv=dx → du=dx/x, v=x. = [x ln x]₀¹ − ∫₀¹ dx = (1·0 − lim_{x→0⁺} x ln x) − 1 = 0 − 0 − 1 = −1. Note lim x ln x=0 by L'Hôpital.
The exact area under the curve from a to b (shaded) is approximated by a few rectangles, the Riemann sum idea behind the definite integral.