Regardless of whether or not God exists, God has no place in mathematics, at least in my book.

Mathematics my foot! Algorithms are mathematics too, and often more interesting and definitely more useful.

Let me also remind you that zero, like all of mathematics, is fictional and an idealization. It is impossible to reach absolute zero temperature or to get perfect vacuum. Luckily, mathematics is a fairyland where ideal and fictional objects are possible.

When a problem seems intractable, it is often a good idea to try to study "toy" versions of it in the hope that as the toys become increasingly larger and more sophisticated, they would metamorphose, in the limit, to the real thing.

The 'lowly' finite is MUCH more beautiful than any 'infinite'

Regardless of whether or not God exists, God has no place in mathematics, at least in my book.

No Victor, you got it backwards, you should evaluate these integrals non-rigorously if you can, and rigorously if you must.