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:
_, _, _, _, 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 .
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?