Homework Help: Surface Integral of Vector Fields

1. Apr 26, 2009

drecklia

Evaluate the surface integral ∫∫S F · dS for the given vector field F and the oriented surface S. In other words, find the flux of F across S. For closed surfaces, use the positive (outward) orientation.
F(x, y, z) = y i + x j + z^2 k
S is the helicoid (with upward orientation) with vector equation r(u, v) = ucos(v)i + usin(v)j + v k, 0 ≤ u ≤ 3, 0 ≤ v ≤ 3π.

∫∫S f*dS=∫∫D F*(r_u x r_v)dA

i got int[0,3] and int[0,3pi] usin(v)^2-ucos(v)^2+uv^2dvdu
i do not know how to integrate this(yeah, shame on me) and i dont know if this integral is correct

2. Apr 26, 2009

Dick

It looks ok to me. What's stopping you from doing it? First integrate dv and then the result du. No special tricks needed. Though you could simplify u*(sin(v)^2-cos(v)^2).