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

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Louis Liu on 10 Sep 2017
Commented: Louis Liu on 10 Sep 2017
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!

Matt J on 10 Sep 2017
Edited: Matt J on 10 Sep 2017
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 on 10 Sep 2017
Thanks!

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