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if \[f(x) = \int\limits_{0}^{x} f(t) dt \]
then f = 0

This is not a true statement.

Michael Spivak claims it is

Who's Michael Spivak?

The man who wrote my textbook.

Whoever he might be, tell him Newton has another opinion :P

This is a direct use of the fundamental theorem of calculus.

\[\int_0^x 2t dt= t^2 \]
\[x^2\]

Oh wait!

haha im not going anywhere with this one

It implies f(0)=0.

hes claiming f(x) = 0 for any x

I certinally dont see it

is there derivative sign infront of integral?

Nope that is the whole question

yes f'(x) = f(x)

We know that\[f(x)=\int f(x)dx\implies f(x)=e^x\]^^

Yeah.

oh nice

I didnt think about e^x with this one

Your statement is still not correct :P

Welllll hold on

it is correct....find c

the e^x makes senese with f'(x) = f(x) but this function is an integral

\[f(0) = \int\limits_{0}^{0} f(t) dt=0\]

It wants me to prove the function is 0

\[\Rightarrow c=0\]

That's right! I'm a loser!! :(

Exactly!

I hate michale spivak :P

I'm just kidding its just a challening course for me

homogeneous differential equation* and it has* *_*

You're welcome! Thanks for fanning me :D