Consider the following double integral with $aa=-12,bb=-6\mathrm{.}7,cc=-10,$ and $dd=4$

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

a$)$ USING MATLAB FOR ALL PARTS Use the mesh function to plot the function $($do not use fmesh$).$ Use the axis command to limit the range of $$ and $yy$ to the

range specified by $aa,bb,cc,$ and $dd.$ Make sure the lower bound for the $z$ axis is $0.$ Use the original upper bound for $zz($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 fprintf 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 $-yy$ plane $($i$.$e$.zz=102)$ 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,

and EL represents the elevation angle in degrees.