Double Integral of Several Functions where Integrand is in Symbolic Array Format

Is there a way to calculate several double integrals simultaneously if the integrand function is first written in symbolic math format? I tried the vpaintegral function in the following way but it didn't work.

Z(x,y)=[f1(x,y) f2(x,y) ...]
INT=vpaintegral(Z,x,[x_start x_end],y,[y_start y_end])

where fi(x,y) are first calculated in a separate symbolic math routine and then assigned to the function Z.

Answer 1

[Areej Varamban Kallan]

Hi Saeid,

In order to perform integration of symbolic functions, you can use the int function from Symbolic Math Toolbox. This function can directly operate on a matrix of symbolic functions too. If you need to do a double integration (say integrate w.r.t x and y), you need to use the int function twice, first integrate your function w.r.t x and then integrate the result hence obtained w.r.t y (or vice-versa). For example, to perform the double integral of f(x,y) =xy over the region (x = 0 to x = 1 and y = 0 to y =1), we can use:

    syms x y
    f = x*y;
    value = int(int(f,x,0,1),y,0,1)
    value =
          1/4

Here the inner integral is w.r.t to x and the outer integral is w.r.t y.

The same applies for a matrix of symbolic functions also, for example

    syms x y
    A = [x + y, x^2 + y^2; x - y, x^2 - y^2];

    value = int(int(A,x,0,1),y,0,1)
    value = 
           [ 1, 2/3]
           [ 0,   0]