1. The problem is to change the order of integration in the triple integral from $r \, dz \, dr \, d\theta$ to $r \, dr \, dz \, d\theta$. 2. The original integral is expressed as $$\int \int \int f(r,z,\theta) \, r \, dz \, dr \, d\theta$$ where the order of integration is $z$ first, then $r$, then $\theta$. 3. To change the order to $r \, dr \, dz \, d\theta$, we need to ensure the limits of integration are adjusted accordingly to maintain the same region of integration. 4. The factor $r$ is part of the volume element in cylindrical coordinates and remains with the $dr$ differential. 5. The new integral becomes $$\int \int \int f(r,z,\theta) \, r \, dr \, dz \, d\theta$$ with the order of integration changed. 6. Remember, when changing the order of integration, the limits of each variable must be carefully re-expressed to cover the same volume. 7. Without specific limits or function, the main step is to reorder the differentials and keep the $r$ factor with $dr$ as $$r \, dr$$. Final answer: The integral changes from $$\int \int \int f(r,z,\theta) \, r \, dz \, dr \, d\theta$$ to $$\int \int \int f(r,z,\theta) \, r \, dr \, dz \, d\theta$$ with appropriate limits adjusted accordingly.