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Question: programming assignment numerical integration in math 1775 last semester...

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Programming Assignment - Numerical Integration 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 2 5 y xx = − 8 shown below. The purpose of this assignment is to increase the accuracy of such approximations of integrals. Write a program (using java) that uses the Midpoint Rule, the Trapezoid Rule, and Simpson’s Rule to find separate approximations to a given definite integral ( ) b a f 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 543 2 f x Ax Bx Cx Dx Ex F ( ) = + + + ++ ; Program outputs should include: • the exact value of the integral, as found using the Fundamental Theorem of Calculus. • values of the approximations for each of the three approximation methods; • the percent error for each method.

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