Wolfram Function Repository
Instant-use add-on functions for the Wolfram Language
Function Repository Resource:
Generate an inactive integral or sum of integrals used for computing the arc length of an expression with given bounds
ResourceFunction["ArcLengthIntegral"][expr,{x,a,b}] returns an inactive integral for computing the arc length of expr for a≤x≤b. | |
ResourceFunction["ArcLengthIntegral"][expr,{θ,a,b},"polar"] returns an inactive integral for computing the arc length of expr for a≤θ≤b in polar coordinates. | |
ResourceFunction["ArcLengthIntegral"][{expr1,expr2,…},{t,a,b}] returns an inactive integral for computing the arc length of the parametric curve defined by {x1[t],x2[t],…}⩵{expr1,expr2,…} for a≤t≤b. | |
ResourceFunction["ArcLengthIntegral"][eqtn,{{x,a,b},{y,c,d}}] returns an inactive integral for computing the arc length of the curve given by implicit equation eqtn for a≤x≤b and c≤y≤d. |
Set up the integral for computing the arc length of a sine wave:
In[1]:= |
Out[1]= |
Activate to compute the full result:
In[2]:= |
Out[2]= |
Set up the integral that computes the arc length of a circle:
In[3]:= |
Out[3]= |
Return the integral for the arc length of a curve given in polar coordinates:
In[4]:= |
Out[4]= |
Return the integral for the arc length of a parametric curve:
In[5]:= |
Out[5]= |
Return the integral for the arc length of the unit circle that is contained within the region bounded by 0≤x≤1 and 0≤y≤1/2:
In[6]:= |
Out[6]= |
You can also leave x or y unbounded:
In[7]:= |
Out[7]= |
Return the integral for the arc length of an asteroid bounded by -1≤x≤1:
In[8]:= |
Out[8]= |
Define and display an implicit region representing two disconnected segments of the unit circle:
In[9]:= |
Out[9]= |
Set up the integrals for disconnected segments of the region:
In[10]:= |
Out[10]= |
Then compute the result:
In[11]:= |
Out[11]= |
ArcLengthIntegral returns the integral for computing the unsigned arc length:
In[12]:= |
Out[12]= |
This work is licensed under a Creative Commons Attribution 4.0 International License