I need to calculate Integral (F . dr), where F(x,y,z) = (z^2, xz, 2xy) and C is the curve obtained from the intersection of the surface z=1-y^2, when z=0 and the plane 2x+3z=6. I'm trying that one for over 5 hours already...

Question

I need to calculate Integral (F . dr), where  F(x,y,z) = (z^2, xz, 2xy) and C is the curve obtained from the intersection of the surface z=1-y^2, when z>=0 and  the plane 2x+3z=6. I'm trying that one for over 5 hours already...

richyw · Answer

hmm. what have you done so far?

anonymous · Answer

so far I've made a sketch of the surface, I calculated curl F and I applied the stoke's theorem to get Integral ( <x, 2y-2z,z>) dS. I have no idea how to move on.

richyw · Answer

wait why is that integral a vector? sorry I am just learning this stuff right now. I'm not even in vector calculus yet. just the basics from multivariable calc. I would like to see how to do this as well!

anonymous · Answer

Over 8 hours trying to solve this problem, still nothing :(

Well, it's a vector integral because the integral is not over a scalar function, but over a vector field ... this stuff is complex. I'll have an exam tomorrow morning (my final) and I can see I'm completely screwed ...

anonymous · Answer

it looks like I can transform this integral I'm left with using this relation : 

(attached image)

I just don't know how to apply this into my integral :(

anonymous · Answer

mainly because I don't know how to calculate the normal of a surface.