S is a portion of a curve with r(u,v)(adsbygoogle = window.adsbygoogle || []).push({});

where 0 < u < 2 and 0 < v < 2pi

I'm meant to calculate Flux of the vector field F

My Calculations

First found dr/du

then dr/dv

Using the cross product, I found N = (- u cos (v) + 5 sin (v), -5 cos (v) - u sin(v), u)

Then I dot product with the given F (after putting it in terms of "u" and "v")

Then I do the relevant integration

I think my method is correct, however since my cross product yields an extremely long vector it makes all my following calculations really tedious.

So just want to check if theres a easy way to do this.

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# Calculating flux through a surface area

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