I have the following homework problem:

In part, we compute both integrals from Stokes' theorem for the helicoid where lies in the rectangle , and is the vector field .

First, compute the surface integral:

, where

_, _, _, _, and

____ (use "t" for theta).

Finally, the value of the surface integral is ____.

Next compute the line integral on that part of the boundary from to .

, where

_, _,

and ____ (use "t" for theta).

----

So far I have a=0, b=pi/2, c=0, d=1, and those are right. But, I'm stuck at ____. I tried finding:

Then I plugged into to get:

I dotted that with the cross product and found:

Which is what I thought should be.. but my webwork says that it is incorrect. Can anyone find where I am going wrong?