How to solve

Part $1$: A Function$(10$ pts$)$

Write a function that computes the area under the

curve using the trapezoidal rule, but using every$-$

other data point.

Function name: calc$\_$trap$\_$odd

Inputs: two: $x$ and $y$ data vectors

Outputs: one: the value of the integral

So the first line take Matlab's default: function

$[$outputArg$1,$outputArg$2]=$

untitled$($inputArg$1,$inputArg$2)$ and change it to

function $[$l$\_$calc$]=$ calc$\_$trap$\_$odd $(x,y)$

This should calculate the integral based on the

concept in this graph:

When you use this function, it might look like this:

$>x=[0$:$\mathrm{.}5$:$]$;

$>y=sin(x)$;

$>I=cal{c}_{t}ra{p}_{o}dd(x,y)$

$I=$

$1\mathrm{.}8213$

Part $2$: Integrating $(10$ pts$)$

A$.$ Find the integral of $I={\displaystyle \underset{2}{\overset{3}{}}}(x+sin(x))dx$ in steps

of $0\mathrm{.}1.$

Solve using trapz $($built$-$in MATLAB function$)$

Solve using calc$\_$trap$\_$odd

Solve using Simpson's $\frac{1}{3}$ Rule

Discuss the differences in the results from the three

calculations.

Formal Plotting program

Write a function that creates an engineering plot of the input data. Sample plot

Function name: ME$\_$plot

Inputs: three: xdata and ydata $-$ vectors of points, a fittedmodel from the Curve Fit App.

Outputs: a complete graph

Data plotted as points

A best fit curve

A title box: title, name, class$/$section or data of collection, best fit equation

if the user selects it$,$ the value of the area under the data

Comments

H$1$ help line

Author and creation date information

Explanations of code and variables as necessary

Function should allow the user to define the text for the various labels. $($use the MatLab command input or inputdlg$)$

Function should be easy to use!! The concept is to walk the user through all the steps they need to get the info added to the graph. You can

Practical analysis. Download this dataset $+-.$ This data represents a stress$-$strain curve of $6061-$T$6$ Aluminum.

You need to determine:

a$)$ plot the data in a proper ME graph, including labels and a curve fit for at least part of the data

b$)$ the Modulus of Elasticity and

c$)$ the Modulus of Toughness

from the experimental data. If you do not recognize these terms, a quick web search $($perhaps from wiki or

instron.us $-$ maker of test equip$)$ should help.

Notes:

Different data sets have different plot symbols

Different lines use different line types

Each data set has its own curve fit $-$ a best fit line that approximates the data

Axes and data are labeled

Title, author, collection info and equations for best fit line are in a title box

Control fonts, colors, legends, grids, etc.

Formal Plotting program

Write a function that creates an engineering plot of the input data. Sample plot darr

Function name: ME$\_$plot

Inputs: three: xdata and ydata $-$ vectors of points, a fittedmodel from the Curve Fit App.

Outputs: a complete graph

Data plotted as points

A best fit curve

A title box: title, name, class$/$section or data of collection, best fit equation

if the user selects it$,$ the value of the area under the data

Comments

H $1$ help line

Author and creation date information

Explanations of code and variables as necessary

Function should allow the user to define the text for the various labels. $($use the MatLab command input or inputdlg$)$

Function should be easy to use!! The concept is to walk the user through all the steps they need to get the info added to the graph. You can

Practical analysis. Download this dataset $+-.$ This data represents a stress$-$strain curve of $6061-$T$6$ Aluminum.

You need to determine:

a$)$ plot the data in a proper ME graph, including labels and a curve fit for at least part of the data

b$)$ the Modulus of Elasticity and

c$)$ the Modulus of Toughness

from the experimental data. If you do not recognize these terms, a quick web search $($perhaps from wiki or

instron.us $-$ maker of test equip$)$ should help.