how can i implement integralN (given by Sir Mike Hosea)

sir, i want to evaluate multiple integration of f(x,y,z,w)= xyzw w.r.t dxdydzdw from x=0 to 1 ,y=0 to 1 ,z=0 to 1 and w=0 to 1 ;by using integralN.m (given by Sir Mike Hosea) so how can i do so?

Answer 1

[Birdman]

Why don't you try the following instead?

syms f(x,y,z,w)
f=x*y*z*w;
fX=int(f,x,0,1)
fY=int(fX,y,0,1)
fZ=int(fY,z,0,1)
fW=int(fZ,w,0,1)

or

syms f(x,y,z,w)
f=x*y*z*w;
res=int(int(int(int(f,x,0,1),y,0,1),z,0,1),w,0,1)

[Sourav Kumar]

thanks Birdman, but for function like f(x,y,z,w)= 1/((x^x)*(y^y)*(z^z)(w*w)),your process will not be applicable; e.g: multiple integration of f(x,y,z,w)= 1/((x^x)*(y^y)*(z^z)(w*w)) w.r.t dxdydzdw from x=1 to 2 ,y=1 to 2 ,z=1 to 2 and w=1 to 2. so how will i evaluate its value?

Answer 2

[Star Strider]

This takes forever and may not converge (I did not let it complete), but at least appears to run:

f = @(x,y,z,w) 1./((x.^x).*(y.^y).*(z.^z).*(w.*w));
f1 = @(y,z,w) integral(@(x) f(x,y,z,w), 1, 2, 'ArrayValued',1);
f2 = @(z,w) integral(@(y) f1(y,z,w), 1, 2, 'ArrayValued',1);
f3 = @(w) integral(@(z) f2(z,w), 1, 2, 'ArrayValued',1);
Q = f3([1 2]);
Result = integral(f3, 1, 2, 'ArrayValued',1);

I will leave it for you to experiment with.