Proof of f(x)=0 for All x in [a,b] via Integral Form

  • Thread starter Thread starter Misswfish
  • Start date Start date
  • Tags Tags
    Analysis
Misswfish
Messages
6
Reaction score
0
Suppose f is continuous function on [a,b] such that for each continuous function g, \int(fg)dj = 0 (Note: integral is from a to b) , then f(x) = 0 for each x in [a,b].

I know that I should use the theorem If is continuous on [a,b], f(x)\geq0 for each x in [a,b] and theree is a number p i n [a,b] such that f(p) > 0, THen \intf dj > 0.

I just don't understand how they tie together.
 
Physics news on Phys.org
Misswfish said:
I know that I should use the theorem If is continuous on [a,b], f(x)\geq0 for each x in [a,b] and theree is a number p i n [a,b] such that f(p) > 0, THen \intf dj > 0.

What is the contrapositive of this statement? It pretty much falls out of it.
 
Ahhh my teacher told me to pick a "clever" g(x) so that we can use this theorem and therefore f(x) = 0. I was thinking contradiction but my teacher shot that down
 
Back
Top