1. ## 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.

2. ## Re: intergral equation consiquence..

Hint : $\frac{d}{dx}\int_a^xf(t)\;dt=f(x)$

3. ## 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?