Project ForgeEngineering Mathematics
Calculus
GATE 2018
Easy
According to the Mean Value Theorem, for a continuous function f(x) in the interval [a,b], there exists a value ξ in this interval such that ∫ₐᵇ f(x)dx =
- f(ξ)(b−a)
- Bf(b)(ξ−a)
- Cf(a)(b−ξ)
- D0
Explanation
This is the Mean Value Theorem for integrals: there exists ξ∈[a,b] such that ∫ₐᵇf(x)dx = f(ξ)(b−a), i.e., f(ξ) equals the average value of f over the interval.
Source: GATE ME 2018 Session 1 (Set 1) (2018)
This question is part of a 15-day revision cycle — sign in and Project Forge will bring it back the day before you'd forget it.