$$\iint_S \sqrt{x^2+y^2} dσ $$
$$ S(x,y,z)= ( x^2+y^2=4,y \geq 0 , z \in [0,5] ) $$
I have this surface integral with the equation of a cylinder in 3d cutted horizontally and to be honest I don't know if what I showed in the picture is correct.(I have no idea where to project the z axis). How do I find the parameters? Are the parameters polar coordinates?
On
I modified @Andrei's answer a little bit.
Use cylindrical coordinates: $$\iint_S\sqrt{x^2+y^2}dS=\int_0^5 dz\int_0^{\pi}r^2d\phi$$ I used $x^2+y^2=r^2$, and the surface element for a constant radius is $dS=r\ d\phi dz$. as $y\geq 0$ then $\phi$ is between 0 and $\pi$. In your case $r=2$. $$\iint_S\sqrt{x^2+y^2}dS=5\cdot2^2\cdot \pi=20\pi$$
Use cylindrical coordinates: $$\iint_S\sqrt{x^2+y^2}dS=\int_0^5dz\int_0^{2\pi}r^2d\phi$$ I used $x^2+y^2=r^2$, and the surface element for a constant radius is $dS=r\ d\phi$. In your case $r=2$. $$\iint_S\sqrt{x^2+y^2}dS=5\cdot2^2\cdot 2\pi=40\pi$$