In Java or MatLab ONLY. Write a program that uses the Midpoint Rule, the Trapezoid Rule, and Simpsons Rule to find separate approximations to a given definite

In MATH 1775 last semester, you used Riemann sums in Excel to approximate the value of the definite integral that represents the area of the region between the x-axis and the graph of y=8x2-r shown below. 10 5- -0.5 0.5 1.5 2.5 The purpose of this assignment is to increase the accuracy of such approximations of integrals Write a program (using a language of your choice) that uses the Midpoint Rule, the Trapezoid Rule, and Simpson's Rule to find separate approximations to a given definite integral j /(x)dx The program should accept the following as user inputs: the limits of integration a and b: the number of subintervals n, which may be as large as one million; the coefficients of an arbitrary 5th-degree polynomial the exact value of the integral, as found using the Fundamental Theorem of Calculus Program outputs should include: values of the approximations for each of the three approximation methods; the percent error for each method