Alternative Programming Assignment Write a program that uses the Midpoint Rule, the Trapezoid Rule, and Simpson's Rule to find separate approximations to the area between the x-axis and the graph of y=8x2x3 from x=0 to x=2. Your program should subdivide the interval [0,2] into an arbitrary number n of subintervals of width x that can be changed by the user. Use your program to compute the required area for n=100 and for n=1000 subintervals, using each of the three methods each time. For each computation, find the percent error in the result. Then write a brief report comparing the accuracy of the three methods for this calculation