Answer on MATLAB please

$2D$ integration

Consider the following double integral with $a=-12,b=-6\mathrm{.}7,c=-10,$ and $d=4.$

${\displaystyle \underset{a}{\overset{b}{}}}{\displaystyle \underset{c}{\overset{d}{}}}133+(\frac{x^5}{32768}+\frac{y^5}{7776})dydx$

a$)$ Use the mesh function to plot the function $($do not use fmesh$).$ Use the axis command to

limit the range of $x$ and $y$ to the range specified by $a,b,c,$ and $d.$ Make sure the lower

bound for the $z$ axis is $0.$ Use the original upper bound for $z($i$.$e$.$ before using the axis

command$).$ You can save the original axes using: $v=$ axis;

b$)$ Calculate an estimate of the integral using a single application of Simpson's $\frac{3}{8}$ rule in each

dimension, starting with the $x$ axis. Use an fprintf statement to print your answer.

c$)$ Calculate an estimate of the integral using a single application of Simpson's $\frac{3}{8}$ rule in each

dimension, starting with the $y$ axis. Use an fprintf statement to print your answer.

d$)$ Calculate the true value of the integral using the int function. Use an fprint $f$ statement

to print your answer.

e$)$ Are the results from b through $d$ the same? Why or why not?

f$)$ Extra Credit $(6$ points$)$ Recreate the plot from part $($a$)$ in a new figure. Add two things to the

plot: $($i$)$ a magenta plane corresponding to a height of $102$ units above the $x-y$ plane $($i$.$e$.z=$

and $($ii$)$ plot all of the points used in part $($c$)$ as red asterisks. Use the view command to

set the view to $AZ=0\mathrm{.}3$ and $EL=24\mathrm{.}2.$ Note: $AZ$ represents the azimuth angle in degrees,