(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Hi

I am converting from Cartesian co-ordinates to cylindrical co-ordinates systems and can do the conversion fine, but am unsure about how to convert the limits.

Q)

Region V is given in Cartesian by: [tex]F(x,y,z) = xi+yj+z(x^{2}+y^{2})k[/tex]

Where [tex]x^{2}+y^{2} \leq 1[/tex]

and [tex]0 \leq z \leq 2[/tex]

2. Relevant equations

[tex] x = \rho cos(\varphi), y = \rho sin(\varphi), z = z[/tex]

[tex] cos^{2}(x)+sin^{2}(x) = 1[/tex]

3. The attempt at a solution

[tex] F(\rho,\varphi,z) = \rho cos(\varphi)\widehat{\rho} + \rho sin(\varphi)\widehat{\varphi} + z\rho^{2}\widehat{z}[/tex]

I know that z has stayed the same as it has not changed, but im not sure how to do the [tex]\rho[/tex] and [tex]\varphi[/tex].

If you could help me on how to do this id really appreciate it.

Many thanks in advance

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# Homework Help: Convert Cartesian To Cylindrical Limits

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