how to calculated integral of multiplying two function handle that changed by loop

hi guys

i have two function like these:

    f(x,y)=(i+1)x+(j-1)y
    g(x,y)=(i-1)x+(j-1)y

(real functions are more complex that here)

now i want to calculate integral of h(x,y)=f*g when f & g change by loops depend on i & j.

i want to write these function in a new mfile & use of them in my code. but i don't know hoe i can do this.

actually i want do like bellow.

    for i=1:n
for j=1:m
h=@(x,y)(f*g)
l=integral2(h,-1,1,-1,1)
end
end

that f & g are functions like this.

    function d=f(i,j)
       f(x,y)=(i+1)*x+(j-1)*y
    end

i know cods are incorrect but wrote these to saying what i want to do.

function are complex & i should use them several times in my code so i cant write them in it.

thank u for answering :)

[Walter Roberson]

for i=1:n
  for j=1:m
    h =@(x,y) f(x,y,i,j) * g(x,y,i,j);
    l = integral2(h,-1,1,-1,1)
  end
end 

function d = f(x, y, i, j)
  d = (i+1).*x + (j-1).*y;
end

Answer 1

[Walter Roberson]

h = @(x, y)  f(x, y).*g(x,y);

[mohammad m]

hi thank you for answering. when i use this code an error like bellow occurred when i edit my code like you.

     Undefined function or variable 'x'.

then for calculate integral of (f*f), i change my code like below :

   for i=1:2
 for j=1:2
h=@(x,y)f(i,j).*f(i,j);
l=integral2(h,-1,1,-1,1)
 end
 end

and function f in another mfile like below

    function d=f(i,j)
       d=@(x,y)(i+1)*x+(j-1)*y
    end

now i get this error:

   Undefined function 'times' for input arguments
of type 'function_handle'.
Error in @(x,y)f(i,j).*f(i,j)
Error in integral2Calc>integral2t/tensor (line
229)
        Z = FUN(X,Y);  NFE = NFE + 1;
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 integral2 (line 106)
    Q =
    integral2Calc(fun,xmin,xmax,yminfun,ymaxfun,opstruct);
  Error in Untitled4 (line 6)
l=integral2(h,-1,1,-1,1)

i don't know how to make new functions by loop & how to multiply them & how to integrate new function. i'm using matlab 2013

Answer 2

[Steven Lord]

A 1-dimensional example:

fun1 = @(x) sin(x);
fun2 = @(y) cos(y);
fun3 = @(z) fun1(z).*fun2(z);
integral(fun3, 0, 1)

To check, explicitly specify the function in the integral call:

integral(@(x) sin(x).*cos(x), 0, 1)

Another check is to perform the integration symbolically with the int function from Symbolic Math Toolbox. The vpa call just displays the answer in a format that's easier to compare with the numeric answers.

syms q
vpa(int(sin(q)*cos(q), q, 0, 1))

[mohammad m]

thank you for answering. my function change by loop & are complex, i'm trying to don't use of syms, because syms reduce speed, so i'm trying to find a way by function handle or any other way that can calculate multiplying & integration of parametric functions that change by loop.