Home » Video Blog » Length Of Arc on the TI-89 App | Every Step Calculus Video

Show Work Step by Step on your TI-89 Calculator Screen

Home » Video Blog » Length Of Arc on the TI-89 App | Every Step Calculus Video

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.

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