PLEASE USE MATLAB AND MAKE CODE COPYABLE

Gauss$-$Legendre

Consider the following integral.

$f(x)={\displaystyle \underset{-2}{\overset{3}{}}}-0\mathrm{.}5x^6-0\mathrm{.}5x^5+1\mathrm{.}6x^4+1\mathrm{.}8x^3+1\mathrm{.}9x^2-0\mathrm{.}9x+379$

a$)$ Plot the function $($integrand$)$ over the interval. Include a solid black line for the $x$ axis $($do not

use the grid function$).$ You may need to use the axis function to make sure that the $x$ axis

line is visible.

b$)$ Calculate the exact value of the integral in MATLAB. Use an fprint f statement to print

your answer with $10$ digits after the decimal point.

c$)$ Use the three$-$point Gauss$-$Legendre method to calculate the integral of the function. Show

all the steps in the method in your code. Do not use any functions you have written or the

built$-$in integration functions. Use an fprint f statement to print the result with $10$ digits

after the decimal point.

d$)$ Why is the true error nonzero for the Gauss$-$Legendre method? Explain in text.