Answer: ∫ f(x) dx from a to b.
- A ∫ f(x) dx from a to b
- B the value f(b) − f(a)
- C the derivative f′(x)
- D the quotient df/dx
Correct answer: A. ∫ f(x) dx from a to b
Explanation: Area = ∫ₐᵇ f(x) dx.
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.