Quote by JJacquelin
In the function sigma(r), if you replace the exopential function (which tends to zero when r tends to infinity) by a linear function which tends to infinity when r tends to infinity), indeed, the result will differ greatly.
So greatly that the integral (from 0 to infinity) is no longer convergent.

What do I do?
The exponential law of density distribution [itex] \sigma (r)) = \sigma_{0} \exp(\frac{r}{L}) [/itex]
I want to apply a linear truncation for [itex] \sigma (r) [/itex]
[itex] \sigma (r) =
\left\{\begin{matrix}\sigma (r),
&r < Rt \\ \sigma (Rt)(1+(Rtr)/SCL),
& Rt < r < Rt+SCL\\ 0,
& r > Rt+SCL
\end{matrix}\right.[/itex]