Question

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 + z2 k S is the helicoid (with upward orientation) with vector equation r(u, v) = u cos v i + u sin v j + v k, 0 ≤ u ≤ 5, 0 ≤ v ≤ 3π

Answer 1

In this question it is quite confusing what is the z component of F. It appears as 2z but may be student want to write it as square of z. Therefore I solved it for both (i.e. for 2z and square of z both).