# Thread: Line Integral and/or Greens Theorem Problem

1. ## Line Integral and/or Greens Theorem Problem

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

2. I was a little confused with the characters you used, but this is what I got from it:

$\int_C xz \,ds$

Where:
$x = (e^{-t}) cos(3t)$
$y = (e^{-t}) sin(3t)$
$z = (e^{-t})$
$0 \le t \le 2\pi$

Then you can use greens theorem:

Hope this helps.
$\int_C x z \, dr = \int_{t_1}^{t_2} x(t) z(t) \, \sqrt{ \left( \frac{dx}{dt}\right)^2 + \left( \frac{dy}{dt}\right)^2 + \left( \frac{dz}{dt}\right)^2} \, dt$.