- #1
farso
- 15
- 0
Homework Statement
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]
Homework Equations
[tex] x = \rho cos(\varphi), y = \rho sin(\varphi), z = z[/tex]
[tex] cos^{2}(x)+sin^{2}(x) = 1[/tex]
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 I am 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