It is rather easy to implement this numerically, as shown in the following code.
// Loop over Monte Carlo trials n
integral =0.;
for ( int i = 1; i <= n; i++){
// Finds a random value for x in the interval [0,3]
x = 3*ran0(&idum);
// Finds y-value between [0,exp(3)]
y = exp(3.0)*ran0(&idum);
// if the value of y at exp(x) is below the curve, we accept
if ( y < exp(x)) s = s+ 1.0;
// The integral is area enclosed below the line f(x)=exp(x)
}
// Then we multiply with the area of the rectangle and divide by the number of cycles
Integral = 3.*exp(3.)*s/n