This applet demonstrates an elementary application of Monte Carlo integration to evaluate a simple integral.

By clicking on the appropriate button, you can evaluate the integral via either the rectangle
rule or Monte Carlo integration. In either case, the number of quadrature points *N* used to estimate the
integral can be varied by changing the value in the box (the largest value accepted is
1000000).

The result of the calculation is then displayed, along with the error in the result (given that
the exact value of the integral is 1). Also, in the figure you will see the x-values used to
perform the quadrature. For the Monte Carlo integration, different points are generated (and a different estimate of the integral is obtained) each time the button is pressed; for the rectangle-rule integration, the values are determined once given *N*, and do not change with each button-press.