I would like to integrate a field $f(r,f)$ (which I don't know it analytically) , where $r$ is the radius and $f$ the angle. I obtained a large set of data located at predefined mesh points $i,j$ e.g. $f(i*dr, j*df)$ where $dr, df$ the spatial increments. From the calculus I know that $$ \iint{f(r,f)rdrdf} $$ is the formula for the surface integral. How can I evaluate this integral, only by using the discrete data? Unfortunately I don't know the function in order to use a Gauss method. Will a sum $$ \sum_{i}\sum_{j}f(idr,jdf)idrdrdf $$ be sufficient?
2026-04-02 20:15:28.1775160928
Numerical integration of discrete data in polar coordinates
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