Hi;

I am trying to use the divergence theorem to calculate the outward flux through a centered sphere of radius "a". If I manually perform the calculation or use the SurfaceIntegrate function, I seem to get the correct answer. However, I cannot seem to get the Integrate function to give me the correct answer, or at least the same answer, and I do not understand why - see attached notebook.

Since the SurfaceIntegrate function and the Integrate functions are very similar, with the exception of the divergence at the beginning of the Integrate functions, it is difficult to understand why the Integrate functions produce different answers. Even checking the documentation has not helped.

I certainly appreciate any advice you could give to help me understand what and why needs to be done to get these functions to produce the correct answer.

Thanks,
Mitch Sandlin