Please help me. I want to integrate the following function from 0 to plus infinity.

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El Houssain Sabour
编辑： Torsten 2023-2-2
syms r r0 sg g(r)=r*exp(-(log(r)-log(r0))^2/(2*sg^2));
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El Houssain Sabour
El Houssain Sabour 2023-2-2
It's also about the integral, which is in the equation. And that's my problem. I can't implement this with Matlab.
Torsten
Torsten 2023-2-2
编辑：Torsten 2023-2-2
As you can see under
https://www.statlect.com/probability-distributions/log-normal-distribution
integral_{r=0}^{r=Inf} r^n * 1/(r*sqrt(2*pi*sigma^2)) * exp(-1/2 * (log(r)-mu)^2 / sigma^2) dr
=
exp( n*mu + 1/2 * n^2*sigma^2)
Both of your two integrals in question follow from this relation for n=2 and n=3.
So your integral becomes
integral_{r=0}^{r=Inf} r^(n-1) * exp(-1/2 * (log(r)-log(r0))^2 / sg^2) dr =
sqrt(2*pi*sg^2) * exp( n*log(r0) + 1/2 * n^2*sg^2)
for n = 2: sqrt(2*pi*sg^2) * r0^2* exp( 2*sg^2)
for n = 3: sqrt(2*pi*sg^2) * r0^3* exp( 4.5*sg^2)

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回答（1 个）

Dr. JANAK TRIVEDI
编辑：Torsten 2023-2-2
Ran in:
syms r r0 sg
g(r) = r * exp(-(log(r) - log(r0))^2 / (2 * sg^2));
int_g = int(g,r,0,inf)
int_g = 
Note that the inf keyword represents infinity. The integral of g(r) is calculated over the interval [0,inf). You can also specify other intervals of integration as needed.

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