Problem with integration need help

Question

Abdulaziz 2013-12-20

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此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/110275-problem-with-integration-need-help

评论： Walter Roberson 2013-12-20

Hi guys,

The next code is to solve an integration. The code will keep running without show any result. Please, need your help if you know the reason.

The code is;

syms T1 T2 r1 r2 r w m k Tb
clc
b=(-4*m*w^2*r1^4)/(k*(r2^2-r1^2));
c1=((T2-T1)+(b*r2^2/4)*(((r2/r1)^2)-1))/(log(r2/r1));
c2=T1-((b*r2^4)/(4*r1^2))-(((T2-T1)+(b*r2^2/4)*(((r2/r1)^2)-1))/(log(r2/r1)))*log(r1);
Tb=(int((((c1*r/2)+(c2/r))*((b*r2^4/4*r^2)+(c1*log(r)+c2))*r),r,r1,r2))/....
   (int(((((-2*w*r1^2)/(r2^2-r1^2))*(r/2))+(((w*r1^2*r2^2)/(r2^2-r1^2))*(1/r)))*r,r,r1,r2));

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Answer 1

Walter Roberson 2013-12-20

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https://ww2.mathworks.cn/matlabcentral/answers/110275-problem-with-integration-need-help#answer_118913

Try breaking Tb up into two pieces, numerator and denominator, so that you can figure out which of the two integrations is giving the problem.

In my tests with a different mathematics system, the integrations were fast.

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Abdulaziz 2013-12-20

Hi Walter your suggestion was really helpful the problem was in the numerator but i still can not find why

Walter Roberson 2013-12-20

在 MATLAB Online 中打开

In both your original equation and the modified one you give about half an hour ago, none of the b, c1, or c2 involve "r". Because of that, you can do the integration just by

syms b c1 c2 r1 r2 r
Tb1 = int((((c1*r/2)+(c2/r))*((b*r2^4/4*r^2)+(c1*log(r)+c2))*r),r,r1,r2);

and then take that result and substitute in the values for b, c1, c2:

b=(-4*m*w^2*r1^4)/(k*(r2^2-r1^2));
c1=((T2-T1)+(b*r2^2/4)*(((r2/r1)^2)-1))/(log(r2/r1));
c2=T1-((b*r2^4)/(4*r1^2))-(((T2-T1)+(b*r2^2/4)*(((r2/r1)^2)-1))/(log(r2/r1)))*log(r1);
Tb = subs(Tb1);

As the integral will be simpler, it is less likely that it will run indefinitely.

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Answer 2

Abdulaziz 2013-12-20

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此回答的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/110275-problem-with-integration-need-help#answer_118918

编辑：Walter Roberson 2013-12-20

在 MATLAB Online 中打开

the code is simplify like next:

clear all 
syms T1 T2 r1 r2 r w m k Tb
clc
b=(-4*m*w^2*r1^4)/(k*(r2^2-r1^2));
c1=((T2-T1)+(b*r2^2/4)*(((r2/r1)^2)-1))/(log(r2/r1));
c2=T1-((b*r2^4)/(4*r1^2))-(((T2-T1)+(b*r2^2/4)*(((r2/r1)^2)-1))/(log(r2/r1)))*log(r1);
Tb=(int((((c1*r/2)+(c2/r))*((b*r2^4/4*r^2)+(c1*log(r)+c2))*r),r,r1,r2));

the processor is running endlessly to solve the integration until i stop it by ctl/c