PLEASE USE MATLAB

Problem $3$

The following integral arises in the study of reaction$-$diffusion equations. It describes the width of repeating patterns in periodic steady state solutions.

$T()={\displaystyle \underset{0}{\overset{1}{}}}\frac{}{\sqrt[\phantom{2}]{F()-F(z)}}dz.$

Here, and $F(x)=\frac{x^2}{2}-\frac{x^3}{3}.($Notice that the variable of integration is $z,$ not $,$ so $$ is just a fixed constant in the integrand.$)$ Save your function $F$ as an anonymous function just as we did in the lectures.

$(1)$ Find $T(0\mathrm{.}95)$ using the function integral $($in MATLAB$)$ or quad $($in python$).$ Save your answer in a variable named A$13.$

$(2)$ Find $T(0\mathrm{.}5)$ using the function integral $($in MATLAB$)$ or quad $($in python$).$ Save your answer in a variable named A$14.$

$(3)$ Find $T(0\mathrm{.}01)$ using the function integral $($in MATLAB$)$ or quad $($in python$).$ Save your answer in a variable named A$15.$