- #1
ElijahRockers
Gold Member
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Homework Statement
Evaluate
[itex]\int\int_{S}\sqrt{1+x^2+y^2} dS[/itex]
S is the helicoid with vector equation r(u,v) = <u cos(v), u sin(v), v>
0<u<2, 0<v<4pi
The Attempt at a Solution
If I replace the term under the radical with its vector equation counterpart, and multiply that by the cross product of the partials of r(u,v) with respect to u and v, i get
[itex]\int_{0}^{4\pi}\int_{0}^{2} \sqrt{1+u^2}u du dv[/itex]
From there I can do a u-substitution (ill just call it a ω-sub so as not to confuse) with ω=1+u2, and dω/2 = udu.
When I work this out, I get
[itex]\frac{4\pi}{3}(5\sqrt{5}-1)[/itex]
But according to the software this answer is incorrect. Anyone notice a mistake?