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.