I've encountered, on Wikipedia (examples below), an integration notation which seems to be prefix-style: the integral sign is immediately followed by the $\mathrm dx$ (or $\mathrm dy$, or what have you), and this is followed by the function to be integrated. Multiple integration is done by multiple prefixes.
I have two questions:
- Does this notation have a name (and perhaps a Wikipedia article)?
- In this prefix notation, are the integrals evaluated left-to-right, or inner-to-outer?
First place I've encountered the notation: Wikipedia on multiple integration. Most relevant bit:
If the domain D is normal with respect to the x-axis, and is a continuous function; then α(x) and β(x) (defined on the interval [a, b]) are the two functions that determine D. Then: $\iint_D f(x,y)\ dx\, dy = \int \limits_a^b dx \int \limits_{ \alpha (x)}^{ \beta (x)} f(x,y)\, dy.$
Second place I've encountered the notation: Wikipedia on integration by parts. Most relevant bit:
Consider the iterated integral: $ \int_a^z \mathrm dx\ \int_a^x \mathrm dy \, h(y). $ In the order written above, the strip of width d is integrated first over the y-direction (a strip of width dx in the x direction is integrated with respect to the y variable across the y direction) as shown in the left panel of the figure, which is inconvenient especially when function h(y) is not easily integrated.