# Normalizing a Modified Gamma Distribution with limits

I am using a modified gamma distribution (MGD) for a particle size distribution of the form

$$n(D) = N_0 D^\mu e^{-\Lambda D^\gamma}$$

where $$N_0$$ is the scale factor, $$D$$ is the particle diameter, $$\mu, \Lambda,$$ and $$\gamma$$ control the shape, and the integral is

$$\int_0^\infty n(D)dD = \frac{N_0}{\gamma}\Lambda^{-\frac{\mu+1}{\gamma}}\Gamma(\frac{\mu+1}{\gamma})$$

In order for the $$N_0$$ term to equal the total particle concentration, I normalize the MGD by its integral as

$$n_{norm}(D) = N_0\frac{D^\mu e^{-\Lambda D^\gamma}}{\frac{1}{\gamma}\Lambda^{-\frac{\mu+1}{\gamma}}\Gamma(\frac{\mu+1}{\gamma})}$$

My question is when I impose size limits on D such that it doesn't go from 0 to $$\infty$$, but something like 2 to 20, how would this normalization change? Is it even possible to normalize it to keep $$N_0$$ in terms of total particle concentration?