You are correct this is a mean value theorem for integrals
See this link
Mean value theorem - Wikipedia, the free encyclopedia
The proof on the wiki page shows you how to select the value you wish.
Hello!
I am working on this problem:
Suppose and are continuous and positive on some interval .
I am trying to show that such that
All I have so far is that since both and are continuous, then their product is continuous (and therefore Riemann-integrable) but I'm not sure how to select this zeta. Whole thing looks like some sort of mean value theorem for products of functions?!
Any help appreciated. Thanks!!
You are correct this is a mean value theorem for integrals
See this link
Mean value theorem - Wikipedia, the free encyclopedia
The proof on the wiki page shows you how to select the value you wish.