Chapter 9, Problem 6P

Areas of Curved Regions the Monte Carlo method can be used to estimate the area under the graph of a function. The figure below shows the region under the graph of $f(x)=x^2$ above the x-axis, between x=0 and x=1. if we choose a point in the square at random, probability that it lies under the graph of $f(x)=x^2$ is the area under the graph divided by the area of the square. So if randomly select a large of points in the square, we have
 

Modify the program from Problem 5 to carry out this Monte Carlo simulation and
mate the required area.