Question

Trying to find the surface area of a helicoid from parametrization. Work attached in screenshot.

Answer 1

No worries. I'm in Calc III, but just *barely*. :)

Answer 2

You need to
evaluate
\[
\int _0^1\int _0^{4 \pi
}\sqrt{u^2+1}
\sqrt{u^2+1}dvdu=\frac{16
\pi }{3}
\]

Answer 3

So I use the parameterization twice?

Answer 4

Nor
\[
\sqrt{x^2+y^2+1}=\sqrt{u^2+1}
\]

Answer 5

Ah, it looks like I missed sqaring the u, for starters. Ok, I'm going to try it again.

Answer 6

\[
\sqrt{u^2 \sin ^2(v)+u^2 \cos
^2(v)+1}=\sqrt{u^2 \left(
\sin ^2(v)+\cos
^2(v)\right)+1}=\sqrt{u^2+1
}
\]

Answer 7

Yes that is what you missed. You did well for a starter

Answer 8

Thank you. I appreciate the confidence booster especially. I've been an A student up until this semester, but between honors physics and Calc III, I've not been feeling terribly smart. :)

Answer 9

On that last one, you have \[\sqrt{u}\] Shouldn't that be \[\sqrt{u^{2}+1}\]

Answer 10

Ah, now I see it.

Answer 11

Ok, took me a while, but I finally got there. Thank you, @eliassaab !

Answer 12

YW. Do not hesitate to tag me for any calc III questions. You can also practice on my Calculus site using Firefox
http://moltest.missouri.edu/calculus.html

Answer 13

Excellent, thank you!