Monte Carlo Integration - Expected value of a function

Hello community,

I estimated this corn production function using data on corn yields and fertilizer

Y = min ( a + b*x , c)

where Y is yield and x is the amount of fertilizer.

Now I want to estimate the expected value of this function using monte carlo integration.

The data I used for estimating this function have x in the range of [0 200].

So I coded this:

%% 
%Define size of sample
n=1000000

%Generate uniformly distributed random numbers in the interval (0,1) and de
u = rand(n,1)

%Define random points in the interval of fertilizer applied [0 200]
f = 200*rand(n,1)

%% Evaluate the function at the different random points  
Y = min( a + b*f , c ); 

%%Obtain the average of the evaluations
meanY = mean (Y)

When I do this I get a pretty reasonable result.

My question is:

Do I have the evaluation of the function at the different random points right?

I've been reading and it seems that I need to correct my evaluation, because my fertilizer data come from the range [0 200] such that the evaluation of the function should be:

Y = 200 * min( a + b*f , c ); 

but when I do this, the value of my expectation (average of the evaluations) does not make sense (it increases 200 times).

Any help will be appreciated.

Thank you!