integral(rho*sqrt(1/(-m*sin(u)^2 + 1)),(u,0,x)) gives a wrong answer
 
  
 
  
 
 
 
 
 
 
    
        
        asked 7 years ago  
 
 epimetheus gravatar image  
 
 
 
 
 
HI everybody,
 
var('x u m')
assume(x>0)
assume(m>0)
assume(m<1)
integral(rho*sqrt(1/(-m*sin(u)^2 +1)),(u,0,x))
 
returns 
 
2*rho*x/m
 
Expected answer is 
 
elliptic_f(x,m)
 
Does anyone know how to fix this ?
 
Thank you.
 
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Comments
What is rho!?
vdelecroix gravatar imagevdelecroix (
    
        7 years ago
    )
rho is a constant
integral(sqrt(1/(-m*sin(u)^2 + 1)),(u,0,x))
returns
2*x/m
epimetheus gravatar imageepimetheus (
    
        7 years ago
    )
Seems a (Maxima) bug.
  • giac and fricas explicitely fail to integrate (retun the unevaluated integral and "failed" respectively
  • mathematica returns the expected result (along with (reasonable) conditions.
  • maple return a suspiciously complicated expression involving elliptic_f, which I was unable to simplify
  • sympy does not return
Worth a ticket  (+ upstream bug report) ?
Emmanuel Charpentier gravatar imageEmmanuel Charpentier (
    
        7 years ago
    )
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