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if you put the differential dx, dy, and dz in the front of the integrand how do you order it so that it matches the order of which variable you want to integrate first?

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- #2

HallsofIvy

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[tex]\int \int \int dxdydz f(x,y,z)[/tex]

implies that you integrate with respect to x first.

- #3

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Another notation which I like very well is to always keep the integral sign and the dx together, sort of an operator notation:

[tex]

\int dz \int dy \int dx \,f(x,y,z)

[/tex]

The integrations are done from right to left.

[tex]

\int dz \int dy \int dx \,f(x,y,z)

[/tex]

The integrations are done from right to left.

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- #4

HallsofIvy

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I personally prefer to put that information on the integral itself. For example

[tex]\int_{x= yz}^z\int_{z= 0}^1\int_{y= z}^{z^2} f(x,y,z)dxdydz[/itex]

I can tell, no matter how "dxdydz" is written, that the "outer integral" is with respect to z since its limits of integration are constants, that the "middle integral" is with respect to y since its limits of integration depend only on z and that the "inner integral" is with respect to x since its limits of integration depend on both y and z.

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