For the surface S (helicoid or spiral ramp) swept out by the line segment joining the point (2t, cost, sint) to (2t,0,0) where 0 is less than or equal to t less than or equal to pi.(adsbygoogle = window.adsbygoogle || []).push({});

(a) Find a parametrisation for this surface S and of the boundary A of this surface.

I can only guess that

x=rcost

y=rsint

z=t

0 less than or equal to t less than or equal to pi

0 less than or equal to r less than or equal to 1

Is this right or totally bogus?

(b) For the vector field F=(x,y,z) compute the flux of F through the surface S. Assume the normal to the surface has a non-negative k component at t=0.

No idea because what is the surface S? It has no equation.

(c) Compute integral (F*dr) where A is the boundary curve of the surface S and F is the force field (x,y,z).

I think I just use Stokes Theorem for (c), but I'm having trouble setting it up since again I have no equation for the surface S. I also don't know how the whole line segment joining works into it.

I can evaluate the integrals, I just have trouble setting them up. If anyone could help me with these three I would appreciate it. Just explain what's going on.

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# Stokes theorem

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