How to define and plot a function containing integrals?

I am trying to create the following function in MATLAB to be used for plotting (see image)

Here is the function I have:

function M = diodeMultiplication(alpha, beta, x, w)

M = (exp(-int(alpha-beta,x,w)))./(1-(int(alpha.*exp(-int(alpha-beta,diff(x),w)),0,w));

end

Where x is a constant (I.e. x = 0) and w is a constant (I.e. w = 1.*10^-4) and alpha and beta are arrays of floating point values that are functions of E.

I would like to input alpha,beta, x and w and plot E vs M. which would look something like this:

plot(E, diodeMultiplication(alpha, beta, x, w));

This function will not run. Does anyone have any input? Thank you.

[Star Strider]

Reference — How can I plot this function that contains integrals?

Answer 1

[Star Strider]

‘... alpha and beta are arrays of floating point values that are functions of E ...’

Having expressions for them is important, since in that situation ‘M’ is then also a function of ‘E’.

Note that using the Sybmolic Math Toolbox (that has the int function) may not be appropriate here, since these integrals may not have analytic solutions, and if int then chooses to use a numeric soluition, would likely be relatively inefficient. It would likely be best to use integral with ‘'ArrayValued',1’, and appropriate expressions for α and β as functions of ‘E’.