(adsbygoogle = window.adsbygoogle || []).push({}); [SOLVED] I want a second opinion

We know the equation

[tex] F=-\frac{dV}{dr}[/tex]

we want to find the integral from [tex]r_{0}[/tex] to [tex]r[/tex].

I have seen someone doing this

[tex]\int^{r}_{r_{0}}Fdr'=-\int^{r}_{r_{0}}\frac{dV}{dr}dr'[/tex]

I am a mathematician and the way I was doing at the university was

[tex] F=-\frac{dV}{dr}\RightarrowFdr=dV[/tex]

and then I integrate

[tex]\int^{r}_{r_{0}}Fdr=-\int^{}_{r_{0}}dV[/tex]

Since the potential depends on r we can integrate. So I would like someone who knows the subject to tell me if the first way is correct since I know the second is correct. Its difficult for me to accept the introduction of another variable r' while we have the r itself.

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# I want a second opinion

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