Requirements:

Write a script and $3$ functions. Write the program to cycle until the users chooses to stop.

The script will have an outer while loop and use dialog boxes and switch case statements as described below.

The three functions are as follows:

$($note a below is the left value of $x$ and $b$ is the right value of $x$ in the interval of interest$)$

a$.$ Integrate a function using the Trapezoidal Method, inputs are $f(x)$ function, $a,b,$ and $n($# of slices$),$ output is the

integral value.

b$.$ Integrate a function using the Simpson Method, inputs are $f(x)$ function, $a,b,$ and $n($# of slices$),$ output is the

integral value.

c$.$ Find the ROOT of a function using the ROOTS algorithm, inputs are $f(x)$ function, $a,b,$ and epsilon$($ a small #

output is the final root of $f(x).$

Script flow should be as follows:

Using a Dialog button with $3$ buttons $($see For$\_$vs $\_$While.m file$)$ have the user chose one of the $3$ anonymous

functions. The selected Anonymous function will be used in the three Programmed functions $(1)$ Integral by

Trapezoidal Method, $(2)$ Integral by Simpson Method, or $(3)$ Root by BiSection Method.:

a$.f(x)=2^{**}{x}^{{?}^{{?}^{?}}}5-3^{**}{x}^{{?}^{{?}^{?}}}2-5($NOTE integral about $206,$ root about $1\mathrm{.}4.$ Method can affect accuracy for both

solutions use $a=1,b=3$ slices and epsilon of your choice but greater than $200$ I recommend $500)$

b$.f(x)=x^{{?}^{{?}^{?}}}2-5($Note you should be able to set any range for integral and a specific range for one of the $2$

roots$)$

c$.$ You pick the $3^{rd}f(x)$ but be sure you can define a range for the roots

Using an input statement ask the user to pick Trapezoidal, Simpson, or ROOT. Make sure you are consistent

with string or number. You can use what you are comfortable with. The input variable will then be used in a

switch case statement. Each case will do the following:

a$.$ First case $($Trapezoidal Integral$)$

i$.$ Ask the user for the inputs $a,b,$ and $nf(x)$ function was already chosen in $1$

ii$.$ Call the function with parameters $f,a,b,n.f$ is $f(x)$ from the anonymous selection above.

iii. Use fprintf to output the answer

b$.$ Second case $($Simpson Integral$)$

i$.$ Ask for the three inputs $a,b,$ and $nf(x)$ function was already chosen

ii$.$ Call the function with parameters $f,a,b,n.f$ is $f(x)$ from the anonymous selection above.

iii. Use fprintf to output the answer

c$.$ Third case $($ROOTs$)$

i$.$ Ask for the three inputs $a,b,$ and $ef(x)$ function was already chosen

ii$.$ Call the function with parameters $f,a,b,e.f$ is $f(x)$ from the anonymous selection above.

Remenber e is a very small # $<mn\; id="EditorElement\_930226">1</mn>$ e$.$g$.{10}^{{?}^{{?}^{?}}}(-6)$ or ${10}^{{?}^{{?}^{?}}}(-8)$

Special NOTE use ${10}^{{?}^{{?}^{?}}}-2,{10}^{{?}^{{?}^{?}}}-6,$ and ${10}^{{?}^{{?}^{?}}}-10$ on $3$ different runs to compare the accuracy of the

answer you get.

iii. Use fprintf to output the answer

Write three functions:

a$.$ Integral by Trapezoidal method

b$.$ Integral by Simpson Method

c$.$ Find Root

These functions inputs and output are described above. The INTEGRATION & ROOT doc describes the algorithm

inside these functions.

EXTRA CREDIT $10$pts: For Item $2$ instead of input statement use a second dialog box with buttons.