Got Homework?
Connect with other students for help. It's a free community.
Here's the question you clicked on:
 0 viewing

This Question is Closed

WalleyeBest 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.MathBest ResponseYou've already chosen the best response.1
This is not a true statement.
 2 years ago

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

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

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

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

imranmeah91Best ResponseYou've already chosen the best response.0
\[\int_0^x 2t dt= t^2 \] \[x^2\]
 2 years ago

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

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

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

imranmeah91Best ResponseYou've already chosen the best response.0
is there derivative sign infront of integral?
 2 years ago

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

Mr.MathBest 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

acrossBest 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

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

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

WalleyeBest 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.MathBest ResponseYou've already chosen the best response.1
You're saying c=0 @Zarkon.
 2 years ago

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

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

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

WalleyeBest 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

WalleyeBest 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

acrossBest 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

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

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

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

WalleyeBest 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.MathBest ResponseYou've already chosen the best response.1
You're welcome! Thanks for fanning me :D
 2 years ago
See more questions >>>
Your question is ready. Sign up for free to start getting answers.
spraguer
(Moderator)
5
→ View Detailed Profile
is replying to Can someone tell me what button the professor is hitting...
23
 Teamwork 19 Teammate
 Problem Solving 19 Hero
 Engagement 19 Mad Hatter
 You have blocked this person.
 ✔ You're a fan Checking fan status...
Thanks for being so helpful in mathematics. If you are getting quality help, make sure you spread the word about OpenStudy.