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.