Suppose that is continuous and for all . Prove that if , then for all .
Attempt
I had attempted to do this problem by contradiction, except I did not understand how to finish the problem. I would appreciate a few helpful hints on this one.
Suppose that is continuous and for all . Prove that if , then for all .
Attempt
I had attempted to do this problem by contradiction, except I did not understand how to finish the problem. I would appreciate a few helpful hints on this one.
From the proof in the fundamental theorem of calculus:
With from given for all
And the definite integral evaluated as from given, then
with confined to be non negative, the summation can only be zero if for all .