code in matlab

3. (40 Points) Construct an algorithm in a function named simpsons that takes three inputs; a function handle the lower bound of the integration and the upper bound of the integration. The function should compute and output the three different approximations of an integral using exactly seven segments. You may call simpson 13 and simpson38 as sub-functions (you must include this in the header). Compute the integral below using each of the methods listed below: |* +0.6x* + 4x + 0.2x+5) dx Value (a) Create a table with the Method, Value, and MTPRE (magnitude of the true percent relative error) for each of the methods below. Include 4 digits to the right of the decimal point in all numbers. Create an anonymous function to calculate the MTPRE (DO NOT put a semicolon at the end). The table should look like the one below. Note that the in the last three lines of the table is a dash (not a minus sign) Method MTPRE Exact TrapSingle Simpsons 1/3 Simpsons 3/8 TrapComposite S13 - 513 - 538 538 - 513 - 313 S13 - S3B - 513 1. Using an anonymous function defined to be the indefinite integral. For example, for f(x) = x2, the function is g(x) = (x". Then the exact or true value of the integral can be computed as low = g(b) - 9(a) where a and b are the Page 2 of 3 88.3458 xxxxxxxx xxxxxxxx xxxx xxxx xxxxxxxx xxxxxxxx xxxx.xxxx xxxxxxxx 0 XXX-XXXX XXX.XXXX xxx.xxxx xxx.xxxx XXX-XXXX XXX XXXX xxxxxxx limits of integration. Do not include a semicolon at the end of the definition of the anonymous function. Do not use the Matlab int function or any similar function ii. A single application of the trapezoidal rule iii. A composite application of the trapezoid rule with n=7 iv. A single application of the Simpson's 1/3 rule v. A single application of the Simpson's 3/8 method, and vi. Three approximations using the composite simpson7 function you created