Calculate complex integral formula

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

Answer 1

[VBBV]

syms x  real
n = 0;
F = log(x+abs(n))./log(x.^2+n.^2);
F3 = vpaintegral(F,x,1,2)

F3 = 

0.5

[VBBV]

define value to n

[Nguyen]

Thank you, I understand your solution but are there another ways to solve the problem

[VBBV]

Ok. Can you tell what specific solution you are looking at inorder to get a value of 0.5 ?

[Torsten]

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