MATLAB: Find finverse of cumtrapz()

functionintegrationMATLABnumerical integration

Hi,
I have to invert the function that calculates cumtrapz of an equation as follows:
    mu = 0;
    var = 1;
    %x = -9:0.01:9;
    syms x
    f(x)  = cumtrapz((2*pi*(v))^(-0.5)* exp(-((x-mu).^2)/(2*(v))))
    i = finverse(f)
    fplot(i)
But this gives me :
f(x) =
0
Warning: Unable to find functional inverse. 
> In symengine
  In sym/privBinaryOp (line 1032)
  In sym/finverse (line 40)
  In inverse_cdf (line 7) 
i(x) =
Empty sym: 0-by-1
However the cumtrapz function does work:
    mu = 0;
    var = 1;
    x = -9:0.01:9;
    y = (2*pi*(v))^(-0.5)* exp(-((x-mu).^2)/(2*(v)));
    i = cumtrapz(y);
    plot(i)
what can i do to invert this function

Best Answer

Since ‘f’: 
mu = 0;
v = 1;
syms x
f(x) = int((2*pi*(v))^(-0.5)* exp(-((x-mu).^2)/(2*(v))))
evaluates to: 
f(x) =
(7186705221432913*2^(1/2)*pi^(1/2)*erf((2^(1/2)*x)/2))/36028797018963968
you will need to use the erfinv function to calculate the inverse.
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