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Student Support Forum: 'Numerical Intgral' topicStudent Support Forum > General > "Numerical Intgral"

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Dima
03/19/13 10:15am

I want to calculate function which is sum of two following integral:
NIntegrate[(1 + (a^4 t x Cos[2 b])/(
Sqrt[c^2 + a^2 t^2] Sqrt[c^2 + a^2 x^2]))/Sqrt[
2 c^2 + (-t + x)^2 + a^2 (t^2 + x^2) -
2 Sqrt[c^2 + a^2 t^2] Sqrt[c^2 + a^2 x^2] Cos[2 b]], {x, -100,
100}, {t, -100, 100}];
NIntegrate[
If[Abs[x - t] < 10^-3,
0, (1 + (a^4 t x)/(Sqrt[c^2 + a^2 t^2] Sqrt[c^2 + a^2 x^2])) /Sqrt[
2 c^2 + (-t + x)^2 + a^2 (t^2 + x^2) -
2 Sqrt[c^2 + a^2 t^2] Sqrt[c^2 + a^2 x^2]]], {x, -100,
100}, {t, -100, 100}]
For default options i got an error so I start playing with methods but get different result for example:
when I calculate this integral with:
, MaxPoints -> 1000000000, Method -> "AdaptiveMonteCarlo", \
PrecisionGoal -> 5, MaxRecursion -> 30
I get result: 6223.43 (for parameters 1, Tan[30 Degree], 13 Degree)
but if I use different method: , PrecisionGoal -> 5, Method -> "LocalAdaptive"
I get different answer: 6229.02.
In both cases there are no errors but answers are significantly different (taking into account that precision goal is 5). Please help me to calculate this integrals correctly for a given precision.


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