Error when doing multidimensional integration using anonymous functions

Question

I am trying to perform multidimensional integration, using the following algorithm:

y= @(a,b,c) a+b+c; %function - 3 dim
y1=@(a,b) integral(@(c) y(a,b,c),-20,20); % L,H - limits for  c`
y2=@(a) integral(@(b) y1(a,b),-20,20); % L,H - limits for b
y3=integral(@(a) y2(a),-20,20); % L,H - limits for a

but this gives the following error:

Error using integralCalc/finalInputChecks (line 515)
Output of the function must be the same size as the input. 
If FUN is an array-valued integrand, set the 'ArrayValued' option to true.

Error in integralCalc/iterateScalarValued (line 315)
                finalInputChecks(x,fx);

Error in integralCalc/vadapt (line 132)
            [q,errbnd] = iterateScalarValued(u,tinterval,pathlen);

Error in integralCalc (line 75)
        [q,errbnd] = vadapt(@AtoBInvTransform,interval);

Error in integral (line 88)
Q = integralCalc(fun,a,b,opstruct);

Error in @(a)integral(@(b)y1(a,b),-20,20)


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

Error in integralCalc/vadapt (line 132)
            [q,errbnd] = iterateScalarValued(u,tinterval,pathlen);

Error in integralCalc (line 75)
        [q,errbnd] = vadapt(@AtoBInvTransform,interval);

Error in integral (line 88)
Q = integralCalc(fun,a,b,opstruct);

Can somebody please help me understand and fix my mistake, or suggest a better method?

P.S.
I know about the integral3 function, but I need this method, because I am going to try 4,5,6.... dimensions later.

Answer 1

I am not sure if this will work in any possible case, but it works quite well for this simple case. Just use symbolic maths.

syms a b c
y=a+b+c;
y1=int(y,c,-20,20)
y2=int(y1,b,-20,20)
y3=int(y2,a,-20,20)

However, careful creating the variables. Don't create yn dynamically!