A community for students.
Here's the question you clicked on:
 0 viewing
Walleye
 3 years ago
Prove that if f(x) = integral from 0 to x of f(t) dt then f = 0
Walleye
 3 years ago
Prove that if f(x) = integral from 0 to x of f(t) dt then f = 0

This Question is Closed

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

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

Walleye
 3 years ago
Best ResponseYou've already chosen the best response.0Michael Spivak claims it is

Walleye
 3 years ago
Best ResponseYou've already chosen the best response.0The man who wrote my textbook.

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

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

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

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

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

Walleye
 3 years ago
Best ResponseYou've already chosen the best response.0I certinally dont see it

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

Walleye
 3 years ago
Best ResponseYou've already chosen the best response.0Nope that is the whole question

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

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

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

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

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

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

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

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

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

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

Walleye
 3 years ago
Best ResponseYou've already chosen the best response.0No 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

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

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

Walleye
 3 years ago
Best ResponseYou've already chosen the best response.0I hate michale spivak :P

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

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

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

Walleye
 3 years ago
Best ResponseYou've already chosen the best response.0ahhh 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!!!!

Mr.Math
 3 years ago
Best ResponseYou've already chosen the best response.1You're welcome! Thanks for fanning me :D
Ask your own question
Sign UpFind more explanations on OpenStudy
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.