MATLAB: How can i use integral2 for a vector-valued function

integral2numerical integration

for example i wrote this code:
 % code
f=@(x,y)x+y;
g=@(x,y)x^2+y^2;
h=@(x,y)x/y+y/x;
w=@(x,y)sin(x)+cos(y);
box=@(x,y)[f(x,y) g(x,y);h(x,y) w(x,y)];            
answers=integral2(box,1,2,1,2)
i expected answers to be a 2*2 scalar matrix but i got only error… what to do?

Best Answer

They’re not 'ArrayValued' in the sense integral understands, and only integral — and not integral2 — can handle array-valued arguments. Otherwise, you could just use integral twice, the second time on the result of the first.
They’re also essentially independent of each other, so integrate them individually using integral2 and then put them together in a matrix at the end.
Specifically:
% Vectorised Equations: 
f = @(x,y)x+y;
g = @(x,y)x.^2+y.^2;
h = @(x,y)x./y+y./x;
w = @(x,y)sin(x)+cos(y);
intf = integral2(f,1,2,1,2);
intg = integral2(g,1,2,1,2);
inth = integral2(h,1,2,1,2);
intw = integral2(w,1,2,1,2);
answers = [intf intg; inth intw]
answers =
     3.0000     4.6667
     2.0794     1.0243
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