In math, the notation of an integral is usually like
$$\int_u^v\!\!\int_a^b\!\!f(x,y)\,dx\,dy\tag{math}$$ where $\int$ and $dx$ are acting as brackets around the function to be integrated. In physics however, a common notation is
$$\int_u^v\!\!\!dy\int_a^b\!\!\!dx\,f(x,y) \tag{phys}$$
What's the purpose of these different notations, and from where do they originate?
The math notation that surrounds the expression to be integrated looks reasonable, whereas the physics notation assumes that one knows how far the expression extends. The physics notation maked it easier to associate variable and rage resp. area (if present) associated to the integral, which might be siperior if the integrand is very complex; however complicated integrands are also not uncommon in math.