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RE: Negative Area

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  • Subject: [mg220] RE: [mg213] Negative Area
  • From: Chip Sample <sample at>
  • Date: Wed, 23 Nov 1994 11:12:10 CST

On integrating a +ve function (A>B) I obtain a -ve

function.  Would you consider this to be a bug?

Integrate[1/(A+B Cos[x])^2,{x,0,2 Pi}]/.{A->2,B->1}
  -4 Pi
3 Sqrt[3]


(rmj at
Since the form of the indefinite integral depends on the values of A and B, the 
proper thing for Mma to do is leave the integral unevaluated.  

Maybe this is related to other complaints that MMa is incapable of keeping 
track of such constraints as A is integer or B >0.  It would seem to need this 
capability to recognize that a pattern match is conditional on such a 

At any rate,  it seems like a good idea to give Mma all the inputs you have up 
front  if possible to avoid this "bug".  I tried:
Integrate[1/(A+B Cos[x])^2/.{A->2,B->1},{x,0,2 Pi}]

  4 Pi
3 Sqrt[3]

apparently the right answer.


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