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$\begingroup$ I think this solves my problem, I just have to look into how this applies in my specific case (I remember that we had that equation in multvariable calc, but I'm bit rusty on that :D). If anyone wants to help me by transforming the integral at hand, it would be appriciated! $\endgroup$
– Ville Alanko
Commented Jan 3, 2023 at 16:01
$\begingroup$ Wonderful! If this actually turns out to solve your problem, feel free to mark the answer as accepted and give it an upvote! I'd love to help you out with the calculations, but that wouldn't be soon since I'm pretty busy in this period $\endgroup$
– Marcello Fonda
Commented Jan 3, 2023 at 22:12

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