three dimensional surface integral

[mathstresser]

Evaluate the surface integral.

\(\displaystyle \L\\\int_{s} \sqrt(1+x^2+y^2) dS\)

S: is the helicod with the vector equation
R(u,v)=ucosvi+usinvj+vk
0<=u<=1
0<=v<=pi

So, I substituted and got
\(\displaystyle \L\\\int_{0}^{1}\int_{0}^{pi} \sqrt(1 + (ucosv)^2 + (usinv)^2) dvdu\)

But, I don't think that's right.

What am I doing wrong?

 

[galactus]

Find \(\displaystyle \L\\\frac{\partial{r}}{\partial{u}}\)

\(\displaystyle \text{and}\)

\(\displaystyle \L\\\frac{\partial{r}}{\partial{v}}\)


\(\displaystyle \L\\\int\int{f(x,y,z)}dS=\int\int{f(x(u,v),y(u,v),z(u,v))\begin{Vmatrix}\frac{\partial{r}}{\partial{u}}\times\frac{\partial{r}}{\partial{v}}\end{Vmatrix}dA\)