Please help, Please look $at$ the error codes $on$ Problem $2$ and problem $3.$ Need the codes $to$ work. Thanks $in$ advance

Problem $3$: Use MATLAB and the integral$3()$ function $to$ evaluate the integral ${\displaystyle \underset{0}{\overset{2}{}}}{\displaystyle \underset{0}{\overset{2}{}}}{\displaystyle \underset{0}{\overset{\sqrt[\phantom{2}]{16-r^2}}{}}}{r}^{2}dzdrd.$ Use the trisurf$()$ function $to$ visualize the region $of$

integration over the rectangular region $R=[-3,3][-3,3][0,4].$

Put your mat$\frac{h}{e}$xplanation here...

$\%$ Define the integrand $in$ cylindrical coordinates

$f=$ @$(theta,r,z)r.{?}^2$;

$\%$Define the $limits$

$thet{a}_{m}in=0$;

$thet{a}_{m}ax=2*pi$;

$r_{m}in=0$;

$r_{m}ax=2$;

$z_{m}in=0$;

$z_{m}ax=$ @$(r)sqrt(16-r.{?}^2)$;

$\%$Evaluate the triple integral

$integra{l}_{v}al=$ integral$3(f,r_{m}in,r_{m}ax,thet{a}_{m}in,thet{a}_{m}ax,z_{m}in,z_{m}ax)$;

Error using MAT$325$ModuleFiveTemplate$>$@$(r)sqrt(16-r.{?}^2).$

Too many input arguments.

Error $in$ integral$3>$@$(y{)}_m$axxy$(x(1)*ones(size(y.).).y).(line132)$

@$(y)zmaxxy(x(1)*ones(size(y)),y),...$

Error $in$ integral$2$Calc$>$tensor $(line202)$

top $=$ YMAX$(x)$; $\%$Visualize the region

$[X,Y,Z]=$ meshgrid$(linspace(-3,3,50),$ linspace$(-3,3,50),$ linspace$(0,4,50))$;

$R=sqrt(X.{?}^2+Y.{?}^2)$;

inside $=(R2)$ & $(Zsqrt(16-R.{?}^2))$ & $(Z0)$;

$\%$Extract the surface points $\%$Visualize the region

$[X,Y,Z]=$ meshgrid$(linspace(-3,3,50),$ linspace$(-3,3,50),$ linspace$(0,4,50))$;

$R=sqrt(X.{?}^2+Y.{?}^2)$;

inside $=(R2)$ & $(Zsqrt(16-R.{?}^2))$ & $(Z0)$;

$\%$Extract the surface points

$[faces,$ vertices$]=$ isosurface$(X,Y,Z,$ inside, $0\mathrm{.}5)$;

$\%$Create the visualization

disp$([\text{'}The$ value $of$ integral $is$: $\text{'},$ num$2str(integra{l}_{v}al)])$;

$\%$ Create the rectangular region

$[x,y,z]=$ meshgrid$(-3$:$0\mathrm{.}1$:$3,-3$:$0\mathrm{.}1$:$3,0$:$0\mathrm{.}1$:$4)$;

$\%$Plot the surface $of$ integration

figure;

trisurf$(x,y,z)$;

xlabel$(\text{'}x\text{'})$;

ylabel$(\text{'}y\text{'})$;

zlabel$(\text{'}z\text{'})$;

title$(\text{'}Regionof$ Integration'$)$;

MAT$325$ModuleFiveTemplate.$mlx\frac{?}{M}$

ATLAB Driv$\frac{e}{M}AT325$ModuleFiveTemplate.$mlx$

Problem $1$: Use MATLAB and the integral$2()$ function $to$ evaluate the integral $of$ the function $f(x,y)=x^3-2y^3$ over the rectangular region $R=[1,2][2,4].$

$f=$ @$(x,y)x.{?}^3-2*y.{?}^3$;

result $=$ integral$2(f,1,2,2,4)$;

fprintf$(\text{'}The$ result $of$ the integral $is$: $\%\mathrm{.}4f$

$\text{'},$ result$)$;

The result $of$ the integral $is$: $-112\mathrm{.}5000$

Problem $2$: Use MATLAB and the integral$2()$ function $to$ evaluate the integral ${}_R(x+y)dA$ over the region $R=\{(x,y)|2\sqrt[\phantom{2}]{x^2+y^2}4,y0\}.$

Put your mat$\frac{h}{e}$xplanation here...

$f=$ @$(x,y)x+y$;

$\%$ Define the region using a characteristic function

integrand $=$ @$(x,y)f(x,y).*(x.{?}^2+y.{?}^{2}4).*(x.{?}^2+y.{?}^{2}16).*(y0)$;

$\%$Set $up$ the rectangular regin that contains our region $of$ interest

result $=$ integral$2(integrand,-4,4,0,4)$;

Warning: Reached the maximum number $of$ function evaluations $(10000).$ The result fails the global error test.

fprintf$(\text{'}The$ result $of$ the integral $is$: $\%\mathrm{.}4f$

$\text{'},$ result$)$;$|$

The result $of$ the integral $is$: $37\mathrm{.}3337$