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Suppose that [itex]f: [a,b] \rightarrow \mathbb{R}[/itex] is continuous and [itex]f(x) \geq 0 [/itex] for all [itex] x \in [a,b][/itex]. Prove that if [itex]\int^b_a f(x)dx=0[/itex], then [itex]f(x)=0 [/itex] for all [itex] x \in [a,b][/itex].
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.
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.