Integration of a function which has limits in terms of parameters

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aakash dewangan 2021-5-12

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https://ww2.mathworks.cn/matlabcentral/answers/828005-integration-of-a-function-which-has-limits-in-terms-of-parameters

评论： Walter Roberson 2021-5-16

采纳的回答： Jan

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Hi,

I have a function f3(t), defined as

clc; clear all;
syms  t L rho m L n T  k  G  v
N(t) = (T*L/2)*(n*pi/L)^2+k*sin(n*pi*v*t/L);
D(t) = (rho*L/2+m*(sin(n*pi*v*t/L))^2);
alpha(t) = N/D;
i = 6; j = 1
f3(t) = alpha(t)*cos(2*pi*i*t/L)*sin(2*pi*j*t/L);
I3 = int(f3,t,0,L)

when i am integrating the function f3(t) from limits 0 to L, the code is not giving me the output in the form of some expression. The output i am getting is in the form of int(f3,t,0,L), which I dont want. I want output in the form of expression (which will contain t L rho m L n T k G v).

Please help me with this!! Any help will be appreciated..

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aakash dewangan 2021-5-15

编辑：aakash dewangan 2021-5-15

Walter Roberson, thanks again for your reply and help.

Yes, you are right. I got integration output for a few combinations of parameter values (not for all values). Thanks for help.

"Do you have any suggestion for me to do this (integration) using any other approach / method / technique??"

Thanks,

Walter Roberson 2021-5-16

I have no suggestions.

There just might be a change of variables available to make sin(n*pi*v*t/L) linear.

Is n*v known to be integer? If so then that would make a difference in the integration, as sin(n*pi*v*t/L) at t=L would be sin(n*pi*v) and if n*v were integer that would be 0 .

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采纳的回答

Jan 2021-5-14

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此回答的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/828005-integration-of-a-function-which-has-limits-in-terms-of-parameters#answer_699678

在 MATLAB Online 中打开

syms t L rho m L n T k G v

N(t) = (T*L/2)*(n*pi/L)^2+k*sin(n*pi*v*t/L);

D(t) = (rho*L/2+m*(sin(n*pi*v*t/L))^2);

alpha(t) = N/D;

i = 6; j = 1;

f3(t) = alpha(t)*cos(2*pi*i*t/L)*sin(2*pi*j*t/L);

I3 = int(f3, t, [0,L])

I3 =

As Walter has said already: There is no closed form solution of this integral. You can simplify it only, if you provide specific values for the parameters.