title: How to evaluate this line integral (Python-Sympy)
body: <p>The idea is to compute the line integral of the following vector field and curve:</p>
  
  <p><a href="https://i.stack.imgur.com/V8wZb.png" rel="nofollow noreferrer"><img src="https://i.stack.imgur.com/V8wZb.png" alt="enter image description here"></a> </p>
  
  <p><a href="https://i.stack.imgur.com/LI5D6.png" rel="nofollow noreferrer"><img src="https://i.stack.imgur.com/LI5D6.png" alt="enter image description here"></a></p>
  
  <p>This is the code I have tried:</p>
  
  <pre><code>import numpy as np
  from sympy import *
  from sympy import Curve, line_integrate
  from sympy.abc import x, y, t
  C = Curve([cos(t) + 1, sin(t) + 1, 1 - cos(t) - sin(t)], (t, 0, 2*np.pi))
  line_integrate(y * exp(x) +  x**2 + exp(x) + z**2 * exp(z), C, [x, y, z])
  </code></pre>
  
  <p>But the ValueError: Function argument should be (x(t), y(t)) but got [cos(t) + 1, sin(t) + 1, -sin(t) - cos(t) + 1] comes up.</p>
  
  <p>How can I compute this line integral then?</p>
  
  <p>I think that maybe this line integral contains integrals that don't have exact solution. It is also fine if you provide a numerical approximation method.</p>
  
  <p>Thanks</p>