Answer: Reversing limits changes sign.
- A Reversing limits changes sign
- B f(x) is odd
- C Integration is linear
- D The antiderivative changes
Correct answer: A. Reversing limits changes sign
Explanation: By the Fundamental Theorem: ∫ₐᵇf(x)dx = F(b)−F(a). Reversing limits: ∫ᵦₐf(x)dx = F(a)−F(b) = −[F(b)−F(a)]. Reversing integration limits negates the value; this property is independent of whether f is odd or even.
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.