(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Evaluate the integral [itex]\int\int_S \sqrt{1+x^{2}+y^{2}}dS[/itex] where S:{ r(u,v) = (ucos(v),usin(v),v) |[itex] 0\leq u\leq 4,0\leq v\leq 4\pi[/itex] }

2. The attempt at a solution

Here is my attempt, I am fairly sure I am right, but it is an online assignment and it keeps telling me I am wrong. I just wanted to double check before I contact the professor to see if he made a mistake.

Let x=ucos(v),y=usin(v) and,

the jacobian determinant is [itex]u(cos^{2}(v)+sin^{2}(v))=u[/itex]

now my new integral is

[itex]\int_0^{4\pi} \int_0^4 u\sqrt{(1+u^{2})} dudv[/itex]

Now this is a fairly straightforward problem and I do a simple substitution to get

let [itex]\phi=1+u^{2},du=2u[/itex]

[itex]\frac{1}{2}\int_0^{4\pi} \int \sqrt{\phi} d\phi dv=2\pi[\frac{2}{3}\phi^{\frac{3}{2}}]=2\pi[\frac{2}{3}(1+u^{2})^{\frac{3}{2}}]_0^4[/itex]

and finally after plugging in the values, I get

[itex]2\pi(\frac{2}{3} 17^{\frac{3}{2}} - \frac{2}{3})[/itex]

Does anyone else see a flaw in this? again, I am pretty sure I am right but would appreciate it immensely if someone could point out my mistake!

Thank you

EDIT: Also if I made any typos in the equations my apologies, this is my first time editing with latex commands

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Evaluate the integral over the helicoid [Surface integrals]

**Physics Forums | Science Articles, Homework Help, Discussion**