I have a homework question that goes like this:
Evaluate ∫c xz ds where C is the curve with parametric equations:
x= e-t cos(3t) y= e-t sin (3t) z=e-t 0 ≤ t ≤ 2π
I was a little confused with the characters you used, but this is what I got from it:
$\displaystyle \int_C xz \,ds$
Where:
$\displaystyle x = (e^{-t}) cos(3t) $
$\displaystyle y = (e^{-t}) sin(3t) $
$\displaystyle z = (e^{-t}) $
$\displaystyle 0 \le t \le 2\pi $
Then you can use greens theorem:
Hope this helps.
-Chad