Numerical integration with two parameters

So I want to integrate the following integral fun = @(t, x, y) (y-t*x+t^2)/(sqrt((x-2*t)^2+(y-t^2)^2)^3). I tried using the quad function (@t from -inf to inf) because the parameters are 'vectors' ie. x=-inf:inf and y=-inf:inf but I don't get an answer. Am I using the correct function or should I do something else, I really can't figure it out. Any answer would be helpful, thanks in advance.

[Torsten]

I tried using the quad function (@t from -inf to inf) because the parameters are 'vectors' ie. x=-inf:inf and y=-inf:inf

So you are trying to calculate the 3d integral for x=-Inf:Inf and for y=-Inf:Inf and for t=-Inf:Inf of the above function ?

Or is it a one-dimensional integral with fixed values for x and y ?

[Dimitar]

Not really, I want to get one more 'vector' of answer with different values of x and y, for example x=0, y=0 the next one being x=0,y=1 etc. And after I get all the answers I want to plot them on a graph Sorry, I don't know how to explain better, I hope you can understand now.

Answer 1

[Torsten]

You should check whether the integral exists when y = x^2/4. In this case, the denominator of fun is 0, and I think you'll have a pole of order 1 at t = x/2. This would mean the integral does not exist.

fun = @(t,x,y)(y-t*x+t.^2)./(sqrt((x-2*t).^2+(y-t.^2).^2).^3);

% Case where y ~= x^2/4
x = 2;
y = 4;
value = integral(@(t)fun(t,x,y),-Inf,Inf)

value = 0.7966

% Case where y = x^2/4
x = 2;
y = 1;
value = integral(@(t)fun(t,x,y),-Inf,Inf)

Warning: Reached the limit on the maximum number of intervals in use. Approximate bound on error is 1.3e-02. The integral may not exist, or it may be difficult to approximate numerically to the requested accuracy.

value = 1.8403

[Dimitar]

I actually succeeded getting results and plotting them, by taking the values of x and y as such: [x, y] = ndgrid(-10:10,-10:10) and adding 'ArrayValued' to the integral function. I just have to figure out how to exclude ie set to 0, the values of the integral where it doesn't exist. Thank you so much!!