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Mathematics Calculus Wolfram Language

Integral takes long time in evaluation

izzy kerszenbaum

Posted 3 years ago

Hi, I am a student of PHYS and new to Mathematica. I am trying to solve the integral shown below, but the program is running already for hours. I didn't think it will take this long for what I thought is a simple double integral. I looked at this for a while and can't find an error w/my code. Is anything wrong with my code? Thanks! Integrate[(k x^3 + b x^4 + c y x^3) - Sqrt[x^2 + y^2] * (k a x^3 + a b x^4 + a c y x^3), {x,0,Sqrt[R^2 - y^2]}, {y,0,R}]

POSTED BY: izzy kerszenbaum

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Mariusz Iwaniuk

Mariusz Iwaniuk, engineer, math hobbyist.

Posted 3 years ago

Try: $Version ("12.3.0 for Microsoft Windows (64-bit) (May 10, 2021)") f = (k x^3 + b x^4 + c y x^3) - Sqrt[x^2 + y^2](k a x^3 + a b x^4 + a c y x^3) Integrate[f, {y, 0, R}, {x, 0, Sqrt[R^2 - y^2]}, Assumptions -> {R > 0}] (-(1/45) k R^5 (-6 + 5 a R) - 1/672 (4 c + 3 b \[Pi]) R^6 (-7 + 6 a R)*)

Try:

 $Version
 (*"12.3.0 for Microsoft Windows (64-bit) (May 10, 2021)"*)

 f = (k x^3 + b x^4 + c y x^3) - Sqrt[x^2 + y^2]*(k a x^3 + a b x^4 + a c y x^3)
 Integrate[f, {y, 0, R}, {x, 0, Sqrt[R^2 - y^2]}, Assumptions -> {R > 0}]

 (*-(1/45) k R^5 (-6 + 5 a R) - 1/672 (4 c + 3 b \[Pi]) R^6 (-7 + 6 a R)*)

POSTED BY: Mariusz Iwaniuk

izzy kerszenbaum

Posted 3 years ago

Thank you Mariusz!! I will try it now.

POSTED BY: izzy kerszenbaum

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