Answer: 16/3.
- A 32/3
- B 4
- C 16/3
- D 8/3
Correct answer: C. 16/3
Explanation: Area = ∫₀⁴√x dx = ∫₀⁴ x<sup>1/2</sup> dx = [(2/3)x<sup>3/2</sup>]₀⁴ = (2/3)(4<sup>3/2</sup>)−0 = (2/3)(8) = 16/3 square units.
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.