Write a program or use a spreadsheet to  find the approximate area or volumes in Problems 3–7 in Section 5.1.

Data from problem 3

Using Monte Carlo simulation, write an algorithm to calculate an approximation to π by considering the number of random points selected inside the quarter circle:

Data from problem 4

Use Monte Carlo simulation to approximate the area under the curve f (x) = √x, over the interval 1/2≤ x≤ 3/2.

Data from problem 5

Find the area trapped between the two curves y = x² and y = 6 – x and the x- and y-axes.

Data from problem 6

Using Monte Carlo simulation, write an algorithm to calculate that part of the volume of an ellipsoid:

Data from problem 7

Using Monte Carlo simulation, write an algorithm to calculate the volume trapped between the two paraboloids: