MATLAB: How to apply numerical integration on a symbolic matrix

integration

Can I use integral2 to calculate the matrix below on the domain[0,1]*[0,1];

My matrix is much more complicated than this one, and I do not want to calculate the symbolic expression one by one~

Best Answer

Please try this is code:

fun = {@(x,y)x+y,@(x,y)x.^2+y.^2;@(x,y)x-y,@(x,y)x.^2-y.^2}
q = cellfun(@(z)integral2(z,0,1,0,1),fun);

or let fs - a your symbolic matrix, then

fun = zeros(size(fs));
for jj = 1:numel(fs)
    fun = matlab2Function(fs(jj));
    out(jj) = integral2(fun, 0, 1, 0, 1);
end

Related Solutions

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

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]

MATLAB: Integration in MATLAB with symbolic integration limits

syms x
y=x^2
f=int(y,1,x) % integration between 1 and x

Best Answer

Related Solutions

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

MATLAB: Integration in MATLAB with symbolic integration limits

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