Answer: 16/3.
- A 8/3
- B 16/3
- C 32/3
- D 16
Correct answer: B. 16/3
Explanation: The two parabolas meet at (0,0) and (4,4); the enclosed area is 16/3.
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.