Monte Carlo Methods

can be computed analytically and the exact value is I = e − 2. We can use this integral as a test case for numerical integration methods, to see how well they are able to approximate I. When the Trapeziodal Rule was applied with step size h = 0.25, the absolute error in the computed, approximate value of I was ca. 0.04. Using Simpson’s Rule with the same step size gave an absolute error of ca. 0.0006. The step size h = 0.25 corresponds to using n = 5 discretization points. You should now compute an approximation to I by using the Monte Carlo method that is described in Hellander’s compendium. Use n = 5 random values. Compare the approximation to the exact value of I. What is the absolute error? Compare to the errors obtained for the Trapezoidal and Simpson’s Rule, respectively. If you repeat the experiments with more and more random numbers, explain how the error will then behave.