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Mathematics Physics

Non Numerical Integration

bastian orthen

Posted 9 years ago

Hello everyone, i have a problem with an integration. I am using Wolfram "Mathematica 10.0 Student Edition" and i want to solve the Integral: Integrate[1/(R^2 + 2 R a Cos[x-y]+a^2)^2,{x, 0 ,2 Pi}, Assumptions -> R > a > 0 && y Element[0, Pi ] ] ] The result should be: (2 Pi (a^2 + R^2))/(R^2-a^2)^3 but when i calculate it, Mathematica always gives me the answer 0. I have seen that this integration works on another computer and now i do not understand why i do not get the correct result. Thank's for your help!

POSTED BY: bastian orthen

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Tanel Telliskivi

Tanel Telliskivi, Classical Mechanics

Posted 9 years ago

Hello, I wonder why the following is not a same? xv1 = Integrate[1/(R^2 + 2 R*a Cos[x - y] + a^2)^2, x, Assumptions -> R > a > 0 && y > 0 && y < \[Pi] && a \[Element] Reals] ((xv1 /. x -> 2 \[Pi]) - (xv1 /. x -> 0)) // FullSimplify (2 (a^2 + R^2) ArcTan[((a - R) Tan[(x - y)/2])/(a + R)])/(a^2 - R^2)^3 - (2 a R Sin[ x - y])/((a - R)^2 (a + R)^2 ((a + R) Cos[(x - y)/2] - I (a - R) Sin[(x - y)/2]) ((a + R) Cos[(x - y)/2] + I (a - R) Sin[(x - y)/2])) 0

Hello, I wonder why the following is not a same?

xv1 = Integrate[1/(R^2 + 2 R*a Cos[x - y] + a^2)^2, x, 
  Assumptions -> R > a > 0 && y > 0 && y < \[Pi] && a \[Element] Reals]
((xv1 /. x -> 2 \[Pi]) - (xv1 /. x -> 0)) // FullSimplify

(2 (a^2 + R^2) ArcTan[((a - R) Tan[(x - y)/2])/(a + R)])/(a^2 - 
   R^2)^3 - (2 a R Sin[
     x - y])/((a - R)^2 (a + R)^2 ((a + R) Cos[(x - y)/2] - 
      I (a - R) Sin[(x - y)/2]) ((a + R) Cos[(x - y)/2] + 
      I (a - R) Sin[(x - y)/2]))

0

POSTED BY: Tanel Telliskivi