Matlab Triple Integration Error. Thank You

Dear guys, I am trying to do a triple integration. But I am not very understand the meaning of error message. could you take a look for it? Thank you so much

The code is

clear all; 
  %%%== just some parameters here ========  
  a=4; 
  la1=1/(pi*500^2); la2= la1*5;
  p1=25; p2=p1/25;
  sgma2=10^(-11);
  index=1;
  g=2./a;
  syms r u1 u2  u3
  powe= -2 
  seta= 10^powe;
  q=pi.*(la1.*p1.^(2./a)+la2.*p2.^(2./a));
  %%%=== parameters end  ================

yi = @(u3,u2,u1) exp(-u3.*(1+2.*...
 (pi./4 - atan(10.*(u3.^2./u1.^2 + u3.^2./u2.^2 + 1).^(1./2))./2    )./...
 ((( (u3./u1).^(a./2) + (u3./u2).^(a./2) + 1    ).^(2./a)).*seta.^(-2./a)))).*...
                exp(-sgma2.*q.^(-a./2).* seta.*u3.^(a./2)./...
 ((( (u3./u1).^(a./2) + (u3./u2).^(a./2) + 1    ).^(2./a)).^(a./2))  );      

          maxF2 =@(u2) u2; 
          maxF3 =@(u3) u3;
         out2 = integral3(yi, 0, Inf , 0,  maxF3 , 0, maxF2)

As you see, u3 is [0, Inf], u2 is [0, u3], u1 is [0, u2]. Error is showing me as

Error using @(u2)u2
Too many input arguments.

Error in integral3>@(y)ZMAXXY(x(1)*ones(size(y)),y) (line 142)
            @(y)ZMAXXY(x(1)*ones(size(y)),y), ...

Error in integral2Calc>integral2t/tensor (line 191)
        top = YMAX(x);

Error in integral2Calc>integral2t (line 56)
[Qsub,esub] = tensor(thetaL,thetaR,phiB,phiT);

Error in integral2Calc (line 10)
    [q,errbnd] = integral2t(fun,xmin,xmax,ymin,ymax,optionstruct);

Error in integral3/innerintegral (line 138)
        Q1 = integral2Calc( ...

Error in integralCalc/iterateScalarValued (line 314)
                fx = FUN(t);

Error in integralCalc/vadapt (line 133)
            [q,errbnd] = iterateScalarValued(u,tinterval,pathlen);

Error in integralCalc (line 84)
        [q,errbnd] = vadapt(@AToInfInvTransform,interval);

Error in integral3 (line 122)
    Q = integralCalc(@innerintegral,xmin,xmax,integralOptions);

Error in ref7_equ11n3 (line 33)
       out2 = integral3(yi, 0, Inf , 0,  maxF3 , 0, maxF2)

What's meaning of 'Error using @(u2)u2 Too many input arguments.' ?? If I change u2,u3's range to real number (e.g. out2 = integral3(yi, 0, Inf , 0, 1000 , 0, 1000). ), then it's working. out2 will be a real number. Thanks for your time!

Answer 1

[Shoaibur Rahman]

Replace out2 by

out2 = integral3(yi, 0, Inf , 0,  @(u3) u3 , 0, @(u3,u2) u2)

If you want to use function handles as the integration limit, then

ymax should be function x, in your case u3

zmax should be a function x and y, in your case u3 and u2, although u3 has no effect

[sun]

It's working! thanks you so much, @ShoaiburRahman Please allow me to ask more. could you please let me know how do you know this? I want to understand more.

In the page of 'doc integral3' , I only see that z, y can be function, but I did not see zmax MUST be function of x and y.

This is the page,

Input Arguments

expand all
fun — Integrandfunction handle
xmin — Lower limit of xreal number
xmax — Upper limit of xreal number
ymin — Lower limit of yreal number | function handle
ymax — Upper limit of yreal number | function handle
zmin — Lower limit of zreal number | function handle
zmax — Upper limit of zreal number | function handle

[Shoaibur Rahman]

It's my pleasure, and thanks a lot for accepting!

Here is a link: http://www.mathworks.com/help/matlab/ref/integral3.html

Go down to the Input Arguments, and click on ymin, ymax, zmin, and zmax to see their acceptable types.

[sun]

Dear ShoaiburRahman, I see this information as below,

You also can specify zmax to be a function handle (a function of x,y) when integrating over a nonrectangular region.

Does this mean zmax MUST be a function of x,y? hmmm. at first time, I think this is not necessary.