Find the area of the surface.

The helicoid (or spiral ramp) with vector equation

$\displaystyle r(u,v) = ucos(v) i + usin(v) j + v k\ 0\leq u\leq 1, 0\leq v\leq \pi $

$\displaystyle r_u = cos(v)i+sin(v)j +0k $

$\displaystyle r_v = -cos(v)i + ucos(v)j + k $

Next i found $\displaystyle |r_u \times r_v| $

and got $\displaystyle 1 + 2u + u^2 $

Im not even sure if this is right, i got confused by the k term (algebra is rusty). Last, i need to take the

$\displaystyle \int\int |r_u \times r_v| dudv $

Im not sure how to take the integral of this, help would be much appreciated.