I cannot make a calculation with the command int
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Hello, I am doing a calculation, but matlab doesn't want to do it with the command int. I have found the solution with other software or using the command trapz, but it is linger and less accurate.
this is the code
syms x
a=int((72290819601*x^2*(x - 1)^10*(x + 1)^10*(261*x^4 - 90*x^2 + 5)^2)/(134217728*(x - 4752731968273649/18014398509481984)^2),x,-1,1)
It gives infinity as result, whereas it is equal to 3831.098 (all the digits in my formula comes from a simplify command in matlab.
I am running Matlab 2010b
Thanks a lot for any suggestion for fixing the problem, otherwise I'll use the longer procedure from trapz
回答(5 个)
Honglei Chen
2012-5-2
looks to me you have a singular point between -1 and 1 at 4752731968273649/18014398509481984. This might be why
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Walter Roberson
2012-5-2
Try increasing your Digits setting. The integral has some large intermediate terms.
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Walter Roberson
2012-5-3
Sorry, I had a disk problem at home a few days ago and had to wipe my disk; I haven't reinstalled my software yet, so I cannot test at the moment.
Sean de Wolski
2012-5-2
When x = 4752731968273649/18014398509481984 or 0.26ish, the denominator is zero, the numerator is not zero and the value is infinite.
In the numerical world, it would fail if this point was evaluated. You just don't have this in your trapz calculation:
Let's make the function in the happy numerical world:
f = str2func(vectorize('@(x)(72290819601*x^2*(x - 1)^10*(x + 1)^10*(261*x^4 - 90*x^2 + 5)^2)/(134217728*(x - 4752731968273649/18014398509481984)^2)'));
And then evaluate it at our trouble point:
f(4752731968273649/18014398509481984)
Boom!
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mortain
2012-5-3
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Walter Roberson
2012-5-11
For that last integral, Maple indicates the answer is
(7186705221432913/36028797018963968)*sqrt(Pi)*sqrt(2)
bym
2012-5-11
FWIW, in matlab (I just learned the simplify 'trick' for integrals)
int((7186705221432913*(x^2 - 1)^2)/(18014398509481984*exp(x^2/2)*(x + 1)^2), -Inf,Inf)/4
Warning: Explicit integral could not be found.
> In sym.int at 64
ans =
int((7186705221432913*(x^2 - 1)^2)/(18014398509481984*exp(x^2/2)*(x + 1)^2), x = -Inf..Inf)/4
>> simplify(ans)
ans =
(7186705221432913*2^(1/2)*pi^(1/2))/36028797018963968
Walter Roberson
2012-5-11
> Digits := 50;
50
> plot(72290819601*x^2*(x-1)^10*(x+1)^10*(261*x^4-90*x^2+5)^2/(134217728*(x-4752731968273649/18014398509481984)^2), x = .2638296 .. .2638297);
![](https://www.mathworks.com/matlabcentral/images/broken_image.png)
The singularity is clearly present, and with 50 digits of precision being calculated, it sure isn't just round-off error in calculating the plot.
Perhaps you are trying to say that round-off error in your generating calculations led to an incorrect formula that you then asked us to integrate? If so then what is the correct formula?
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