## Length Of Arc on the TI-89 App | Every Step Calculus Video

#### Raw Transcript

#### This is one of my fabulous videos on length of an arc and let’s get started uhm again second, second alpha to get the letters so you can go index and then alpha eight closed parenthesis press enter and here’s my menu you can scroll up to anything you want burt we’re going to do length of an arc right now so were, that’s the number s so you can push alpha s on there too if you knew the program and needed to get there quick which I’m going to do right now. These are position vectors because they’re radius and time and ahh that’s what arc’s are and ahh this is the in vector form the r t form

r t coordinates for vectors x to the t, y to the t, z to the t and we’ll enter them now you have to push alpha again to enter the thing I got the examples up here in a test or on a homework whatever uhm let’s go alpha eight times t I always like to put times in there not just eight t calculator won’t compute that sometimes but I’ve found sometimes it didn’t so I do it all the time and then I’m safe and uhm alpha minus three times t and alpha seven times t shows you what you’ve entered here’s the vector you’re entering for the r t formula and I say it’s ok and so now we go to the r t formula which you have other ones acceleration, linear equation, parametric equations speed, unit tangent vector, velocity all these different choices right now we want length of arc so I’m going to press number three here on the calculator you can see it’s a integral with r prime t that’s the derivative, first derivative of t r t over the area of a, or the range of a and b dt and here’s the formula Length is going to be equal to this here’s the formula for it and the position vector is r t and the i coordinate the j coordinate the k coordinate and we start eight i minus three j and seventeen k keep going we have eight t and the derivative of eight t is eight derivative of minus three t is minus three and derivative of seven t is seven so you have eight squared minus three squared seven squared dt and over the time they want the range so we’re going to go alpha maybe two to the range of alpha nine shows the range over two over nine here’s the formula again put this all on your paper exactly as I show ahh the derivative of eight t is eight and the, ahh that squared is sixty four and here’s nine here’s forty nine there four sixty four, nine, forty nine and that computes out to the square root of one twenty two and one twenty two is square root of course is to the exponent one half and over nine and two area, area so substitute two for t two times this and nine times that and we have that we come up with approximately seventy seven point three the exact is seven time the square roof of one twenty two units two minus the nine that’s how you get that you always take the maximum range and subtract the minimum range from it and here’s seventy seven three eight pretty neat huh go back and do anything you want here velocity, what ever there will be another videos on those ahh everystepcalculus.com. Enjoy my programs you’ll love them.

## Arc Length Calculus Video | y=sin(x) | Simpson’s Rule on the TI89

**Raw Transcript**

This is a video from everystepcalculus.com demonstrating how my programs work on a TI-89, Titanium calculator and other calculators in the TI system for physics and calculus problems so we’re going to do the arc length with regards to sine or cosine and ahh first of all I’m gonna do on the calculator and show you on the calculator how this works you can do arc length here you’ll notice that when you press f three function you come up with that menu you press eight and it’ll go to arc length we’re going to put in sin of x for our function and then a comma with regard to x and then a comma with regard to the ah range of zero and pi you notice it’s busy here that means it’s thinking and the takes a while hard for the calculator to do evidently and here’s the answer three point eight two units so now let’s uhm get started on my programs your going to have to put second alpha to put the letters i n d e x in here. Then press alpha again to put nine and the open and closed parenthesispress enter and we’re into my menu we’re gonna do six which is arc length of a function of f of x which which is this which sine is and we’re gonna enter the function gonna press alpha you have to push alpha before you do anything in the entry lines here enter anything in there so alplha we’re gonna put sine of x I always ask you if it’s ok ahh case you made a mistake and so here’s the arc length formula you’ll notice you’re doing the derivative squared here and the regular function is the original function is sin of x we’re gonna enter our range here over the range of alpha zero and alpha pi I again ask you if it’s ok and then we do the derivative you write this stuff all on your paper as you see itand here’s the derivative of sine of x squared over that range here’s the simpson’s rule which you have to write on your paper I don’t think this problem would ever be on a test it’s too difficult might bemight be in your homework here’s the reality of this of that formula this took me two days to figure this out probably took simpson two years without calcuators and we’re gonna do six intervals let’s take six intervals of that change of x is equal to b minus a divided by the number of itinerations that equals point five two four and that divided by three which is simpson’s rule is point one seventy five this is the change of x and you do each one of these individually it starts with zero etcetera you keep adding this in your paper and the answer is three point eight units as you sum up all these. Pretty neat huh? everystepcalculus.com. Go to my site buy my progams and pass calculus.

## Arc Length Tutorial on the TI-89

RawTranscript

This is a program on arc length, and let’s get started. To get my code in here to get my menu to come up, you have to put the letters i n d e x, which you do by pressing 2nd alpha, on the Titanium first for the letters and then alpha and you can enter the eight and closed parenthesis on there, press the enter button and you are into my menu. Here’s all the choices goes way down here, you can find all kinds of things on here which will help you out in your test, your homework, or just leaning about it, because its so perfect step by step, and it’s all what we wished we could have when we were looking on how to do a problem. That’s why I did it for myself first and now am offering it to you. Let’s do arc length, were going to press the number four here and get into the parametric form which is the r t form with time and radius, and three variables x y and z in this one. And this one is the Cartesian system which is equal to y = f of x, either one will give you the function there. And so we’re going to press two and enter a function. Press alpha and let’s put the function in here, we’re going to go, x cubed divided by six plus one divided by parenthesis two times x, closed parenthesis and over the range of – we have to add alpha again to get the range in here – we’re going to do it, one half to the upper range of two. It shows you what you’ve added here so you can correct it if it’s wrong or check it out here. I say it’s ok so we’re going to press one – derivative of the function here, with respect to x is x squared over two, minus one over two x squared. Here’s the formula for the arc length, the integral over the range of a and b, the square root of one plus dy dx squared, and with the respect of x. Here we have the function into the formula here, this is the part that was squared, here’s what we did the dy dx part, which we found before, mark all of this on your paper of course. Here we’ve taken the square of that, still have the square root to do, one plus, but we’re going to take the square first, like you would in normally doing a problem, here we added the one to it, here we’re going to do the square root of it, which is this. Working the formula through, here’s the, as we integrate it, here’s what the integration is over the range of two and minus one half. We put the two in the problem, two to the four minus three over six times two, which I show you here, equals thirteen twelve’s and we put the one half in here, we subtract the lower from the upper, and we added the half into the formula, here’s minus forty-seven forty-eight. And we can see that we had a minus forty seven, this will trip you up a lot of times, where there’s a minus to a minus, I do it to make sure it doesn’t happen to me, when I’m doing the problem. Thirteen twelve’s plus forty seven forty eight, the answer is thirteen sixteenths, approximately two point zero six two five, rounded to the fifth place. So pretty neat huh, everystepcalculus dot com, check out my other fabulous programs, you’ll love them, worth every penny that you buy it for, so cheap compared to the thousands of hours I’ve spent on this stuff studying it for you, to make sure they are correct and everything, and remember it encompasses calculus two and three and one, so you are buying all three semesters of your calculus in one purchase, ahh have a good one.

## Arc Length

Arc Length in Calculus with the TI-89: Raw Transcript

This is a program on arc length, and let’s get started. To get my code in here to get

my menu to come up, you have to put the letters i n d e x, which you do by pressing 2nd alpha, on the Titanium first for the letters and then alpha and you can enter the eight and

closed parenthesis on there, press the enter button and you are into my menu. Here’s

all the choices goes way down here, you can find all kinds of things on here which will

help you out in your test, your homework, or just leaning about it, because its so perfect

step by step, and it’s all what we wished we could have when we were looking on how

to do a problem. That’s why I did it for myself first and now am offering it to you.

Let’s do arc length, were going to press the number four here and get into the parametric

form which is the r t form with time and radius, and three variables x y and z in this one.

And this one is the Cartesian system which is equal to y = f of x, either one will give

you the function there. And so we’re going to press two and enter a function. Press alpha

and let’s put the function in here, we’re going to go, x cubed divided by six plus one

divided by parenthesis two times x, closed parenthesis and over the range of – we have

to add alpha again to get the range in here – we’re going to do it, one half to the

upper range of two. It shows you what you’ve added here so you can correct it if it’s

wrong or check it out here. I say it’s ok so we’re going to press one – derivative

of the function here, with respect to x is x squared over two, minus one over two x squared.

Here’s the formula for the arc length, the integral over the range of a and b, the square

root of one plus dy dx squared, and with the respect of x. Here we have the function into

the formula here, this is the part that was squared, here’s what we did the dy dx part,

which we found before, mark all of this on your paper of course. Here we’ve taken the

square of that, still have the square root to do, one plus, but we’re going to take

the square first, like you would in normally doing a problem, here we added the one to

it, here we’re going to do the square root of it, which is this. Working the formula

through, here’s the, as we integrate it, here’s what the integration is over the

range of two and minus one half. We put the two in the problem, two to the four minus

three over six times two, which I show you here, equals thirteen twelve’s and we put

the one half in here, we subtract the lower from the upper, and we added the half into

the formula, here’s minus forty-seven forty-eight. And we can see that we had a minus forty seven, this will trip you up a lot of times, where there’s a minus to a minus, I do it to make

sure it doesn’t happen to me, when I’m doing the problem. Thirteen twelve’s plus

forty seven forty eight, the answer is thirteen sixteenths, approximately two point zero six

two five, rounded to the fifth place. So pretty neat huh, everystepcalculus dot com, check

out my other fabulous programs, you’ll love them, worth every penny that you buy it for,

so cheap compared to the thousands of hours I’ve spent on this stuff studying it for

you, to make sure they are correct and everything, and remember it encompasses calculus two and three and one, so you are buying all three semesters of your calculus in one purchase, ahh have a good one.