Integrate a FunctionUsing Simpson’s Integration in MATLAB

Question

This problem involves developing a program to numerically integrate a functionusing Simpson’s integration.

a) Develop a script & supporting functions that performs the following

a. Inputs the stop (t) and the desired error tolerance (tol).

b. Implements the function g(x),

𝑔𝑥 = 3𝑥! + 2𝑥 + 1

c. Plots g(x)

d. Implements a function that integrates g(x) from 0 to t using Simpson’s algorithm.

e. Calls the MATLAB internal integration routine (integral or quad for older versions of MATLAB) function to evaluate the integral.

f. Uses tic and toc to time both the Simpson and integrate calls

g. Determines the error relative to the exact solution. Hint: See notes for using Wolfram Alpha to calculate the integral.

h. Display the run time along with the result and the error (Numerical-Exact)/Exact.

b) Run the script and record the output for t = 5 and TOL = 1e-6.

Summary

This question belongs to MATLAB software and discusses about integrate a functionusing Simpson’s integration in MATLAB.