The surface is defined by with no condition on x. So use x and z as parameters. x= u, , z= v.
I am trying to find the surface area.
So I know that once I have the parameters, I can find Tu, Tv and cross them to find the normal vector.
However, I seem to have trouble whenever the function isn't given in terms of u and v.
This is the problem I am looking at:-
Calculate [Double Integral] f(x,y,z)dS for the given surface and function
y=9-z^2, 0<=x<=3, 0<=z<=3, f(x,y,z) = z
I've got a new problem.
Verify Stokes Theorem for the given vector field and surface, oriented with an upward pointed normal.
F = <2xy, x,y+z>, the surface z = 1 - x^2 -y^2 for x^2 +y^2<=1
For using line integrals, what should I use my c(t) as?
For the Stokes theorem part, I can calculate the curl, but again I don't know how to go from there (as in find the boundaries and dS).