MATLAB: I wanted to solve a parametric double integral. Matlab requires me to set these parameters (for the case x0, x1, x2, x3, x4, x5, x6, x7, x8 and x9). The variables are r and t. Is there a solution with Matlab to solve a double integral set without s

parametric

I wanted to solve a parametric double integral. Matlab requires me to set these parameters (for my case x0, x1, x2, x3, x4, x5, x6, x7, x8 and x9).
The variables are r and t.
Is there a solution with Matlab to solve a double integral set without setting any values of the parameters.
here is the code:
————————————
 syms t r x0 x1 x2 x3 x4 x5 x6 x7 x8 x9;
 tmin = 0; 
 tmax = 1; 
 rmin = 0; 
 rmax = 2*pi; 
 g = +(x0*cos(-2*t)-x5*sin(-2*t))*(1-r^(-2))+(x1*cos(-1*t) - x6*sin(-1*t))*(1-r^(-1))+(x2*cos(0*t)-x7*sin(0*t))*(1-r^(0))+(x3*cos(1*t)-x8*sin(1*t))*(1-r^(1))+(x4*cos(2*t)-x9*sin(2*t))*(1-r^(2));
 h = +(x0*sin(-2*t)+x5*cos(-2*t))*(1-r^(-2))+(x1*sin(-1*t)+x6*cos(-1*t))*(1-r^(-1))+(x2*sin(0*t)+x7*cos(0*t))*(1-r^(0))+(x3*sin(1*t)+x8*cos(1*t))*(1-r^(1))+(x4*sin(2*t)+x9*cos(2*t))*(1-r^(2));
 f = r*(g^2+h^2);
 fun = @(t,r) f; 
 format long 
 J = integral2(fun,tmin,tmax,rmin,rmax,'Method','iterated','AbsTol',1e-12 ,'RelTol',1e-10)
—————end——————-
thank you in advance

Best Answer

You are already using syms so you have the symbolic toolbox. Use int() to do the integration.
int(int(f, t, tmin, tmax), r, rmin, rmax)
The result cannot be a numeric value because of the free variables.
Note: the solution is going to be +/- infinity depending on the value of some of the x* coefficients, because you have r^(-2) and 0 is in the range of r: you have singularities in your integral.
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