Cauchy Mean Value Theorem for Integrals
If are continuous with , then some satisfies .
Proposition 4.28 (Cauchy Mean Value Theorem for Integrals)
Let be continuous, and for all , then such that
Proof
Apply the Cauchy Mean Value Theorem to
there is with
where dividing by is legitimate.
Related
Stated in
- Proposition 4.28 (Cauchy Mean Value Theorem for Integrals)§4.4 Integration and Differentiation