Calculate complex integral formula

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Nguyen
Nguyen 2023-4-23
编辑： Torsten 2023-4-23
Ran in:
syms x n
F = log(x+abs(n))/log(x.^2+n.^2);
F3 = int(F,x,1,2);
limit(F3,n,inf)
ans = 
If I run the code, i will receive limit(int(log(n + x)/log(n^2 + x^2), x, 1, 2), n, Inf) but I want it to be a specific value which is 0.5, how can I do it. Sorry for my bad English

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VBBV
VBBV 2023-4-23
Ran in:
syms x real
n = 0;
F = log(x+abs(n))./log(x.^2+n.^2);
F3 = vpaintegral(F,x,1,2)
F3 = 
0.5
  4 个评论
显示 2更早的评论
VBBV
VBBV 2023-4-23
编辑：VBBV 2023-4-23
Ok. Can you tell what specific solution you are looking at inorder to get a value of 0.5 ?
Torsten
Torsten 2023-4-23
编辑：Torsten 2023-4-23
The OP wants his code to return 0.5 instead of repeating the problem in "ans".
There was another question of the same kind the OP deleted meanwhile.
I wonder if these homework problems are really meant to be solved with MATLAB or theoretically.
For the above question:
The sequence of functions
g_n(x) = log(x+n)./log(x.^2+n.^2)
converges uniformly on [1;2] to 1/2 as n -> Inf.
Thus integration and taking limit can be interchanged:
lim(n -> Inf) integral_{x=1}^{x=2} g_n(x) dx =
integral_{x=1}^{x=2} lim(n -> Inf) g_n(x) dx =
integral_{x=1}^{x=2} 1/2 dx = 1/2

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