# Finding f(x) from given f'(x)

• songoku

#### songoku

Homework Statement
Find f(x) where ##f(x)=\frac{\cos x}{x}## and f(3) = 4. State the answer in form of ##f(x)=\int_{t=p}^{t=q} (........)##
Relevant Equations
Fundamental Theorem of Calculus
This is my attempt:
$$f(x)=\int_{t=p}^{t=x} \frac{\cos t}{t} dt$$

But I am not sure what ##p## is and what the use of ##f(3)=4##

Thanks

You forgot about the constant that is added to the integral. If you start the integral at p=3, then you know that the integral part is 0 at x=3. So what constant is added to the integral?

songoku and Delta2
Homework Statement:: Find f(x) where ##f(x)=\frac{\cos x}{x}## and f(3) = 4. State the answer in form of ##f(x)=\int_{t=p}^{t=q} (...)##
Did you forget to add the prime? Shouldn't it be ##f'(x) = \frac{\cos x}{x}##?

songoku, Delta2 and berkeman
You forgot about the constant that is added to the integral. If you start the integral at p=3, then you know that the integral part is 0 at x=3. So what constant is added to the integral?
I understand

Did you forget to add the prime? Shouldn't it be ##f'(x) = \frac{\cos x}{x}##?
Yes, I am sorry

Thank you very much FactChecker and Mark44