# Repeated integrals

1. Jan 27, 2007

### Jheriko

Is there some notation for an iterated integral, like there is for summations and products?

e.g.

$$\overset{m}{\underset{n=0}{\raisebox{-0.07in}{\Huge{\texttt{I}}}}} f(x_0,x_1,x_2,\ldots,x_m) dx_n$$

$$\overset{m}{\underset{n=0}{\raisebox{-0.07in}{\Huge{\texttt{I}}}^{b}_{a}}} f(x_0,x_1,x_2,\ldots,x_m) dx_n$$

Here I have used "I" to stand in for whatever the correct symbol might be...

2. Jan 27, 2007

### dextercioby

If the integral is a volume integral in "n" dimensions (n>=3), then one can put only one integral sign, but specify the fact that the integration is not in one dimension (as one could assume, once he sees only one symbol of integration) through the measure. In this case a volume integral is an iterated integral. Treating hypersurface integrals is not any different, as one could use only one symbol, even if the # of dimensions is not 1.

3. Jan 27, 2007

### Jheriko

So for a 'hypercubic volume integral' over 0 ... 1 in m dimensions, I could do:

$$V = \prod^{m}_{n=0} [0,1]$$

$$\int_V f(x_0,x_1,x_2,\ldots,x_m) dV$$

Thanks.