- #1

ElijahRockers

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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+u

^{2}, 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?