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Say you have a function, which in cylindrical coordinates it gives that

[tex]\int\int\int \sqrt{x^2 + y^2} dx dy dz[/tex]

which is

[tex]\int\int\int r^2 dr d/theta dz[/tex]

i want to find in cylindrical coordinates, in the area limited by the functions :

[tex]x^2 + y^2 = z^2[/tex]

z is greater or equal than -1 and less than equal to 1.

so, i solve it, but then i realize:

why is the value of solving the inner integral in order to dr (with limits of integration from 0 to z) different that the one in order to dz (with limits from 0 to r), with the middle one being dz or dr, respectively, with limits 0 to 1, and the outside one (d theta) 0 to 2pi?

(all multiplied by two)

the order shouldnt matter, i think.

please explain what the order should be and why, im really confused on this one... thanks

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# Homework Help: Calculating a volume through cylindrical coordinates

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