- #1
jdz86
- 21
- 0
Homework Statement
Let f : [a,b] [tex]\rightarrow[/tex] [tex]\Re[/tex] be continuous and assume f [tex]\geq[/tex] 0. Prove that if [tex]\int_{[a,b]}[/tex]f = 0 then f = 0.
Homework Equations
Nothing really. If relevant, mean value theorem was discussed in earlier problems, so I'm not sure if it fits though.
The Attempt at a Solution
I tried using the MVT and stating that if all that was mentioned above holds true then you can say f(c)(b-a) = 0, then solving b = a. From there I couldn't go anywhere. Pretty sure I wasn't on the right track to begin with in the first place anyway.