I am estimating $\theta$, where $\theta=\int_0^1 f(x)dx, \ \text{where}\ f(x)=x*e^{x/2}$
From a unifrm distibution I generate 1000 random numberers from 0 to 1, $x_1,x_2,...x_{1000},$.
$\hat{\theta}= 1/1000 * \sum_{i=1}^{1000}f(x_i) $
Henc, I am taking the average.
How do I construct a Confidence Interval for $\hat{\theta}$? Say 95%.
As far as I can read from Wikipedia, I think my method is called Monte Carlo integration but I am not sure.