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Question: construct an algorithm in a function named simpsons7 that takes...

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Construct an algorithm in a function named simpsons7 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 simpson13 and simpson38 as sub-functions (you must include this in the header). Compute the integral below using each of the methods listed below:

int_{-5}^{5}(0.075x^5+0.6x^4+0.2x^2+0.5) dx
(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 Value MTPRE 88.3458 Exact TrapSingle Simpsons 1/3 Simpsons 3/8 TrapComposite 513 S13 S38 538 - S13 - S13 513 - S38 - S

i. Using an anonymous function defined to be the indefinite integral. For example, for f(x) = x2, the function is g(x)=(rac{1}{3})x^3 . Then the exact or true value of the integral can be computed as trueg(b) - gl a) where a and b are the 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.

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