I am trying to understand the book, when it says that: "Integrating between time 0 and time T, we get.."

What I need to integrate is this: $\frac{d S}{S}=\mu d t$

And when this is integrated between 0 and T, the book states that we get: $S_{T}=S_{0} e^{\mu T}$

I have tried solving this by doing definite integration, but I have no idea how to get to this result.

If you find that some information is missing in the post, it is because i didn't know, and probably why i couldn't figure it out.


1 Answer 1


Your integral should look equivalent to $$ \int_{S_0}^{S_T} \frac{dS}{S}= \mu\int_{0}^{T}dt $$ where $S$ has been labelled with subscripts corresponding to the time. The left-hand-side is a "standard" integral ( a log).


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