Create a local user defined function, UBArea which will estimate the area from a data set:

Arguments to the function will be:

an array of $\backslash ($ x $\backslash )$ values and

an array of y values

Calculations

Within the function, identify how many data pairs have been provided.

Use a for loop to calculate the area of each rectangle and sum the areas to estimate to total area under the curve.

Return the estimated area

Define a piecewise continuous function, MYFunction such that:

Arguments:

X

Calculations:

If $\backslash ($ X $\backslash )$ is less than or equal to $-5\mathrm{.}5$

$\backslash (\backslash$mathrm$\{$Y$\}=0\mathrm{.}2^\{*\}\backslash$mathrm$\{$X$\}+4\mathrm{.}1\backslash )$

If $\backslash ($ X $\backslash )$ is greater than $-5\mathrm{.}5$ but less than or equal to $5\mathrm{.}5$

$\backslash (\backslash$mathrm$\{$Y$\}=0\mathrm{.}08^\{*\}\backslash$mathrm$\{$X$\}^\{\backslash$wedge$\}2+5\mathrm{.}42\backslash )$

If $\backslash ($ X $\backslash )$ is greater than $5\mathrm{.}5$

$\backslash (\backslash$mathrm$\{$Y$\}=-0\mathrm{.}4^\{\backslash$star$\}\backslash$mathrm$\{$X$\}+5\mathrm{.}2\backslash )$

Return the value of $\backslash ($ Y $\backslash )$

Using the MATLAB editor, create a script $\backslash ($ m $\backslash )-$file for the following:

Define a variable K with values assigned over the range $-20\mathrm{.}5$ to $13\mathrm{.}0$

Define: J $=$ MYFunction$($K$)$

Estimated area under the MYFunction curve accurate to $4$ significant digits

Begin by assigning $\backslash (\backslash$mathrm$\{$N$\}=501\backslash )$ number of data points to be created

Assign preset value to UpperBound $=1$

Assign preset value to LowerBound $\backslash (=0\backslash )$

Using a while loop

while $($UpperBound $>$ LowerBound$)$

Assign values to K

Calculate values for J

Calculate the UpperBound $=$ UBArea$(\backslash (\backslash$mathrm$\{$K$\},\backslash$mathrm$\{$J$\})\backslash )$ and LowerBound $=$ LBArea$(\backslash (\backslash$mathrm$\{$K$\},\backslash$mathrm$\{$J$\})\backslash )$

Round the UpperBound and LowerBound to $4$ significant digits

Increase number of data points $\backslash ($ N $\backslash )$ by $500$

end

Create a x$-$y scatter plot of the K$-$J data with title and labels.

Present the estimate of area