Can someone help me with the following one?
I need to calculate the mass of the surface $x+y+z=a $ , $a>0$ intersected with the cylinder $x^2 + y^2 = R^2 $ where the density is $ u(x,y,z)= (x^2+y^2)^2 + z $ .
As far as I know, I need to calculate : $ \iint_S u(x(u,v),y(u,v),z(u,v)) \,du\,dv $ where $(x(u,v), y(u,v), z(u,v))$ is the parameterization of our surface .
Can someone help me find the parameterization of such a surface?
Please help me. I'm really frustrated. Thanks !