Multiple Integrals: What They Do & How to Understand Them

[Grogerian]

I'm just curious of what exactly multiple integrals are for example if you have
$$\int^{3}_{1}xdx$$
you get 3-1[i think - it's been a while] but what does the second integral or 3rd and so on do to the function, I've looked ahead in my solutions manual and i think i understand part of it :D but id like to know / understand it a bit better it gave me this(from memory - my book isn't in front of me).

$$\int\int(x,y)(x^{2}dx+y^{2}dy) = \int(x^{2})*\int(y^{2})$$

so all you're doing is splitting up x and y into separate integrals? - which doesn't make sense to me but :)

 

[waht]

You have to integrate over one variable at a time. So if are integrating over x first, treat y as a constant. Once you are done with the first integral, integrate over y and treat x constant.