Answer: 1/6.
- A 1/6
- B 1/3
- C 1/2
- D 2/3
Correct answer: A. 1/6
Explanation: ∫₀¹ (√x − x) dx = 2/3 − 1/2 = 1/6.
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.