I'm confused with limits of integrating and which to integrate first,(adsbygoogle = window.adsbygoogle || []).push({});

I've been getting by so far with just knowing the following,

[itex] \int_0^1\int_0^y f(x,y) dxdy = \int_0^1\int_0^{rsin\theta} f(rcos\theta,rsin\theta) rdrd\theta [/itex]

But what happens when we switch it around?

[itex] \int_0^1\int_0^{x} f(x) dydx = ...? [/itex]

Will it still be the same? That is,

[itex] = \int_0^1\int_0^{rcos\theta} f(rcos\theta,rsin\theta) rdrd\theta [/itex]

Thank you for your time!

edit: I suppose it would be, since the assignment of the particular characters x and y are arbitrary. I'm still confused since I'm not showing it explicitly. I need to review Jacobians I suppose, very short on time this weekend though.

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# Cartesian/Polar Integration

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