For a function y=f(x) ,the area under the curve is given by $\int y(x) dx$.
This must mean that the infinitesimal area is $da = y(x)dx$ where y(x) is a finite value, i.e., not an infinitesimal.
However, in solving physics problems involving integration, I usually think "Oh, it's an area integral so there should be two infinitesimal quantities multiplied..." and then I go on to choose the right coordinate system and find the area:
$da= dr rd\theta$ or $da=dx dy$ and so on, where there are two infinitesimals clearly.
Is there a gap in my learning about infinitesimal areas? How is it that the infinitesimal area is first degree infinitesimal in one and a second degree infinitesimal in the other? (Hoping the word "degree" is used properly)