# Numerical integration

• Dazedandconfu

#### Dazedandconfu

ok, I'm not completely sure which section this goes into, but since I'm using this to solve a PDE ima going to put it in here,
I need to integrate w(x,y,z)*V(x,y,z) over a cylindrical domain, it would be fairly simple if V had a "formula" describing the function, but i only have V as a number at a bunch of points(1000 points or so) inside the domain(and on the boundary), w is any C2 function which is zero on the boundaries and not identically zero inside.
I chose a function w and found its values at the same points as V is known, but I'm not sure which is the best way to find an approximation to this integral, any help much appreciated, as always.

Mathematica has a function to generate an interpolation of data points. You could use that and then just numerically integrate the interpolated function. See "Interpolation". Otherwise, if your data is uniformly spaced, why not just construct a Riemann sum on the data:

$$\iiint\approx \sum_{n=1}^{1000} f(r,\theta,z) \Delta V$$

where:

$$\Delta V=r\Delta r\Delta\theta\Delta z$$

hmm, the data is non uniformly spaced, so the riemann integral cannot be done (without interpolation), so i suppose i'll have to generate a interpolation, and then numerically integrate, thanks!,