How to use fsolve to solve the simultaneous equations with integral format?

Hello, I am try to solve the simultaneous equations with integrand recently, but I am stuck now, below is the detail:

The simultaneous equations that I want to solve:

and I write some code like this:

kursi = 1; b1 = 3*1.33+1; b2 = 3*1+1; alpha = 0.05; beta = 0.10;

fun1 = @(t,c0,n) chi2cdf( (n-1)*(b1*sqrt(n)-t).^2./(9*n*c0.^2),n-1 )...
    *( normpdf(t+kursi*sqrt(n))+normpdf(t-kursi*sqrt(n)) );

fun2 = @(t,c0,n) chi2cdf( (n-1)*(b2*sqrt(n)-t).^2./(9*n*c0.^2),n-1 )...
    *( normpdf(t+kursi*sqrt(n))+normpdf(t-kursi*sqrt(n)) );

eq = @(c0,n) [ integral( @(t)fun1(t,c0,n),0,b1*sqrt(n) )-(1-alpha);...
    integral( @(t)fun2(t,c0,n),0,b2*sqrt(n) )-beta ];

result = fsolve(eq,[0,100]);

the feedback from Matlab:

Not enough input arguments.

Error in
@(c0,n)[integral(@(t)fun1(t,c0,n),0,b1*sqrt(n))-(1-alpha);integral(@(t)fun2(t,c0,n),0,b2*sqrt(n))-beta]

Error in fsolve (line 230)
            fuser = feval(funfcn{3},x,varargin{:});

Caused by:
    Failure in initial objective function evaluation. FSOLVE cannot continue.

===================================================================== After comparing to the doc fsolve, I guess the problem are function handle and integral. Does anyone can give me some advices? Thanks!

Answer 1

[Matt J]

The problem is in the way your are passing the unknown input parameters. It should be as a single unknown vector,

result = fsolve(@(p) eq(p(1),p(2)) ,[0,100]);

I would also mention that if p(2)=n is meant to be a discrete variable, fsolve will not handle that. It treats all unknowns as continuous variables.

[Louis Liu]

@Matt J Thanks for your advice! I can get the value now but I need to think again the property of variable n...

[Matt J]

You're welcome, but please click Accept if we've covered your original question.

[Louis Liu]

@Matt J Hello, Can you tell me the initial value of fsolve, [0,100] is the starting point of p(1),p(2) respectively or the interval for p(1),p(2) ? Thanks!

[Matt J]

It is the starting point.

[Louis Liu]

Thanks!