problem with solving integral

Dear all,

I am trying to solve a symbolic integral via matlab.

But I just got the modifed form of my integral as the answer.

What is the problem?

The integral is getting from a popular paper and should not be any problem in it.

I want to reproduce the results of the paper.

T=10.;
mu=0.;
mustar = 400.;
Lambda = 602.3;
GsLambda2 = 2.319;
Gs = 0.00000639;
m0 = 5.5;
m = 100.;
Gv = 0.5 * Gs;
Gd = 0.75 * Gs;
syms p d
int(p.^2.*(((1.-2.*((exp (( sqrt (( sqrt (p.^2.+m.^2.) - mustar ).^2 + ...
d.^2))/T) +1).^(-1)))/(sqrt (( sqrt (p.^2.+m.^2.) - mustar).^2 + d.^2))) + ...
    ((1. - 2.*((exp (( sqrt (( sqrt (p.^2 + m.^2) + mustar).^2 + d.^2))/T)...
    + 1).^(-1)))/(sqrt (( sqrt (p.^2+m.^2) + mustar).^2 + d.^2)))), p, 0, 602.3)

ans =

int(-p^2*((2/(exp((((p^2 + 10000)^(1/2) - 400)^2 + d^2)^(1/2)/10) + 1) - 1)/(((p^2 + 10000)^(1/2) - 400)^2 + d^2)^(1/2) + (2/(exp((((p^2 + 10000)^(1/2) + 400)^2 + d^2)^(1/2)/10) + 1) - 1)/(((p^2 + 10000)^(1/2) + 400)^2 + d^2)^(1/2)), p, 0, 6023/10)

I would really appreciate it if some one could help me.

Answer 1

[Star Strider]

I suspect that the paper did not have an analytical expression for the integral, or you would be evaluating it.

Integrate it numerically instead:

T=10.;
mu=0.;
mustar = 400.;
Lambda = 602.3;
GsLambda2 = 2.319;
Gs = 0.00000639;
m0 = 5.5;
m = 100.;
Gv = 0.5 * Gs;
Gd = 0.75 * Gs;
% syms p d
dfcn = @(d) integral(@(p) p.^2.*(((1.-2.*((exp (( sqrt (( sqrt (p.^2.+m.^2.) - mustar ).^2 + ...
d.^2))/T) +1).^(-1)))./(sqrt (( sqrt (p.^2.+m.^2.) - mustar).^2 + d.^2))) + ...
    ((1. - 2.*((exp (( sqrt (( sqrt (p.^2 + m.^2) + mustar).^2 + d.^2))/T)...
    + 1).^(-1)))./(sqrt (( sqrt (p.^2+m.^2) + mustar).^2 + d.^2)))), 0, 602.3, 'ArrayValued',1);

d = 0:1000;                                                       % Create Values For ‘d’

Result = dfcn(d);

figure
plot(d, Result)
grid

.

[Mahboubeh Shahrbaf]

Thank you very much Star Strider.

So you think there is no way to find an expression for the integral as a function of "d" ?

Here, numerical solving is not appropriate to me.

You know, this integral is a part of a system of integral equations.

Since they are all complicated integrals, I found it easier to solve the integral indefinitely at first

and then use all expressions for the integrals in the systam of nonlinear equations for finding the unknowns variables. "d" is one the unknown variables which I have to find it.

In attached photo, I am now trying to solve the integral in Eq. (37) and "d" is \Delta_MF.

Then it would be so nice if I can estimate every integral with an expression.

[Star Strider]

Well, I did not see this in time and Walter posted an Answer using your updated information (not available in your original post), so I will stop here.

My only Answer is the one I already supplied. I would evaluate ‘d’ and then plug it in, however you choose to solve this.

[Walter Roberson]

I did not use updated information; I just converted the floating point numbers to symbolic numbers and then played around to see what I could get. I posted the result temporarily because the new Run facility would not let me copy out a result line from the previous; had to Submit to be able to copy it.

[Walter Roberson]

I would have to look more closely... but the new equations you posted do not look to me to be the same as the code.

With the code that was posted, I think there is no realistic hope of coming up with a symbolic integral in d.

[Mahboubeh Shahrbaf]

Actually, the integral in the code is exactly the same as one which is in the equation I've posted.

Just I ignored the constant coefficients.

OK, thank you both Star Strider and Walter Roberson.

Then, I have to find another routine to solve directly the integral equations.