General question about integration

[iScience]

when we do partial derivatives we use the curly ∂ to represent a partial change in something w/ respect to a partial change in something else. but say we have an integral with the integrand as a function of (x,y). why do we not use the curly ∂ as the differential when we integrate?

example..

why is it proper to write
∫2xydx

as opposed to this?

∫2xy∂x

 

[BucketOfFish]

When integrating with respect to two or more variables which may vary independently, it is common to use a path integral, where each variable in the path is parametrized through a single common integration parameter. I have never seen a case where the notation you have indicated was necessary. However, it was a very interesting question and made me have to think for a while. Bravo!

 

[lurflurf]

∂ is used sometimes