I have an analytic function defined over x=[0,100] and y=[0,100]. I do not know the precise workings of the function, just that it is smooth, takes in inputs (x,y) and returns a scalar.
It is quite straightforward to numerically integrate this function over a rectangular domain using the function integral2. However, I would like to integrate the function over a circle. For simplicity's sake let's have it centered at (x,y)=(50,50) with a radius of 10.
How would I be able to achieve this? Remember I cannot modify the function by substituting x = 50+10*cos(theta) and y=50+10*sin(theta).
An example function below.
func = @(x,y) x^3*y+x*y^2;