title: How to Integrate Arc Lengths using python, numpy, and scipy?
body: <p>On another <a href="https://math.stackexchange.com/questions/433094/how-to-determine-the-arc-length-of-ellipse">thread</a>, I saw someone manage to integrate the length of a arc using mathematica.They wrote:  </p>
  
  <pre><code>In[1]:= ArcTan[3.05*Tan[5Pi/18]/2.23]
  Out[1]= 1.02051
  In[2]:= x=3.05 Cos[t];
  In[3]:= y=2.23 Sin[t];
  In[4]:= NIntegrate[Sqrt[D[x,t]^2+D[y,t]^2],{t,0,1.02051}]
  Out[4]= 2.53143
  </code></pre>
  
  <p>How exactly could this be transferred to python using the imports of numpy and scipy? In particular, I am stuck on line 4 in his code with the "NIntegrate" function. Thanks for the help! </p>
  
  <p>Also, if I already have the arc length and the vertical axis length, how would I be able to reverse the program to spit out the original paremeters from the known values? Thanks!</p>