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Walleye
Group Title
Prove that if f(x) = integral from 0 to x of f(t) dt then f = 0
 2 years ago
 2 years ago
Walleye Group Title
Prove that if f(x) = integral from 0 to x of f(t) dt then f = 0
 2 years ago
 2 years ago

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Walleye Group TitleBest ResponseYou've already chosen the best response.0
if \[f(x) = \int\limits_{0}^{x} f(t) dt \] then f = 0
 2 years ago

Mr.Math Group TitleBest ResponseYou've already chosen the best response.1
This is not a true statement.
 2 years ago

Walleye Group TitleBest ResponseYou've already chosen the best response.0
Michael Spivak claims it is
 2 years ago

Mr.Math Group TitleBest ResponseYou've already chosen the best response.1
Who's Michael Spivak?
 2 years ago

Walleye Group TitleBest ResponseYou've already chosen the best response.0
The man who wrote my textbook.
 2 years ago

Mr.Math Group TitleBest ResponseYou've already chosen the best response.1
Whoever he might be, tell him Newton has another opinion :P
 2 years ago

Mr.Math Group TitleBest ResponseYou've already chosen the best response.1
This is a direct use of the fundamental theorem of calculus.
 2 years ago

imranmeah91 Group TitleBest ResponseYou've already chosen the best response.0
\[\int_0^x 2t dt= t^2 \] \[x^2\]
 2 years ago

Walleye Group TitleBest ResponseYou've already chosen the best response.0
haha im not going anywhere with this one
 2 years ago

across Group TitleBest ResponseYou've already chosen the best response.0
It implies f(0)=0.
 2 years ago

Walleye Group TitleBest ResponseYou've already chosen the best response.0
hes claiming f(x) = 0 for any x
 2 years ago

Walleye Group TitleBest ResponseYou've already chosen the best response.0
I certinally dont see it
 2 years ago

imranmeah91 Group TitleBest ResponseYou've already chosen the best response.0
is there derivative sign infront of integral?
 2 years ago

Walleye Group TitleBest ResponseYou've already chosen the best response.0
Nope that is the whole question
 2 years ago

Mr.Math Group TitleBest ResponseYou've already chosen the best response.1
I didn't read the question well at first. This means that f is an antiderivative of itself, if I'm seeing this right.
 2 years ago

Walleye Group TitleBest ResponseYou've already chosen the best response.0
yes f'(x) = f(x)
 2 years ago

across Group TitleBest ResponseYou've already chosen the best response.0
We know that\[f(x)=\int f(x)dx\implies f(x)=e^x\]^^
 2 years ago

Walleye Group TitleBest ResponseYou've already chosen the best response.0
I didnt think about e^x with this one
 2 years ago

Mr.Math Group TitleBest ResponseYou've already chosen the best response.1
Then differentiate both sides you get, f'(x)=f(x), which is an ODE that has the solution \(f(x)=ce^{x}\).
 2 years ago

Mr.Math Group TitleBest ResponseYou've already chosen the best response.1
Your statement is still not correct :P
 2 years ago

Walleye Group TitleBest ResponseYou've already chosen the best response.0
Welllll hold on
 2 years ago

Zarkon Group TitleBest ResponseYou've already chosen the best response.4
it is correct....find c
 2 years ago

Walleye Group TitleBest ResponseYou've already chosen the best response.0
the e^x makes senese with f'(x) = f(x) but this function is an integral
 2 years ago

Mr.Math Group TitleBest ResponseYou've already chosen the best response.1
You're saying c=0 @Zarkon.
 2 years ago

Zarkon Group TitleBest ResponseYou've already chosen the best response.4
\[f(0) = \int\limits_{0}^{0} f(t) dt=0\]
 2 years ago

Walleye Group TitleBest ResponseYou've already chosen the best response.0
It wants me to prove the function is 0
 2 years ago

Zarkon Group TitleBest ResponseYou've already chosen the best response.4
\[\Rightarrow c=0\]
 2 years ago

Mr.Math Group TitleBest ResponseYou've already chosen the best response.1
That's right! I'm a loser!! :(
 2 years ago

Walleye Group TitleBest ResponseYou've already chosen the best response.0
No you're not! So basically because f'(x) = f(x) I can say f(x) = ce^x and then show that f(0) = 0 implying that c=0 so f = 0
 2 years ago

Walleye Group TitleBest ResponseYou've already chosen the best response.0
makes perfect sense! Im just be a loser now but how do we know there is no other function s.t. f'(x) = f(x)
 2 years ago

across Group TitleBest ResponseYou've already chosen the best response.0
Mr. Michale Spivak did a good job, that is, to elicit eager students to congregate and think this one through. xd
 2 years ago

Walleye Group TitleBest ResponseYou've already chosen the best response.0
I hate michale spivak :P
 2 years ago

Walleye Group TitleBest ResponseYou've already chosen the best response.0
I'm just kidding its just a challening course for me
 2 years ago

Mr.Math Group TitleBest ResponseYou've already chosen the best response.1
Lol @across. @Wall, this is a first order homogeneous equation and had only this solution, \(i.e f(x)=ce^{x}\).
 2 years ago

Mr.Math Group TitleBest ResponseYou've already chosen the best response.1
homogeneous differential equation* and it has* *_*
 2 years ago

Walleye Group TitleBest ResponseYou've already chosen the best response.0
ahhh yes! I really like this problem! I can't believe I didnt realize f(x) had to be some form of e^x Thanks for all the help everyone!!!!
 2 years ago

Mr.Math Group TitleBest ResponseYou've already chosen the best response.1
You're welcome! Thanks for fanning me :D
 2 years ago
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