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Math Help - intergral equation consiquence..

  1. #1
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    intergral equation consiquence..

    f,g are continues funtion on [a,b]
    prove or desprove by counterexample that:
    if \int_{a}^{x}f(t)dt=\int_{a}^{x}g(t)dt then f=g on [a,b]
    ?

    how i tried:
    i this its correct
    i transfered to the other side
    \int_{a}^{x}f(t)dt-\int_{a}^{x}g(t)dt=0
    \int_{a}^{x}f(t)-g(t)dt=0
    what now?

    i cant do derivative here
    because if i could the i just could do a derivative on both sides from the start
    but it looks to easy thus it is a wrong move.
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  2. #2
    MHF Contributor FernandoRevilla's Avatar
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    Re: intergral equation consiquence..

    Hint : \frac{d}{dx}\int_a^xf(t)\;dt=f(x)
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  3. #3
    MHF Contributor
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    Re: intergral equation consiquence..

    i know that if i do derivative i get
    f(x)-g(x)=0
    and get g(x) to the other side

    but i just coud frpm the start to do a derivativeon both sides a get the asked result even straight forward
    why its not possible?
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