If you only need to find the area shared by two normal distributions, this can be done using an anonymous function, normpdf, and integral.
myNormalDistribution = @(x) min(normpdf(x, 0, 1), normpdf(x, 1, 1))
integralValue = integral(myNormalDistribution, -inf, inf)
integralValue will now contain the total area of the intersection of the two normal distributions (0.6171). This can be visualized with the following code:
x = -3:0.01:3;
plot(x, normpdf(x, 0, 1), x, normpdf(x, 1, 1))
hold on
area(x, myNormalDistribution(x))
The plot from the above code is shown below.
