What is the Use of the Constant in the Integral?

[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

 

[FactChecker]

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?

 

[Mark44]

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]

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