Hello everyone, Tom from everystepcalculus.com and everystepphysics.com. We’re talking about arc length today. Got this on a new test that somebody sent me so I’m going to do a video of it right now. Pretty complicated nonsense in calculus but still there for calculus two, people. So let’s do it, index 8, type in into the home screen there to get to my main menu. Your going to choose number 5, arc length and because the problem gives it an x, or a g a y. I’m going to choose number 2. And we’re going to, I show you the formula here, here’s the formula for the arc length and the x function given is, you have to press alpha before
you enter anything into my entry lines here. Alpha y cubed divided by 6 plus one divided by 2 times y. Looks good. I always show you which of entered, you can change it if you want. I say it’s good. I choose number 1, okay. I always show you the derivative first; take the derivative of that. I give you the choice of which system they give you too. If they give you y, then we’re cool in this system here. We just enter what they give you. If they entered x then you have to compute the y values that were given the X values. So we’re gonna do alpha 2 or, lower one is alpha 2, upper limit is alpha 3, or range, upper range. And I show you that also in case you made a mistake. I say it’s ok. We do our computations. This shows you the exact problem which is what you’re dealing with and what you write down in your paper, here. And we’re going to square that as part of the functions, here. You notice that calculus is so pathetic that they do one derivative and the rest of it is you have to do square roots, you have to do squares, you have to do integrals. Well, I do that all for you. Here’s squared. Now we’re going to add one to what we’ve squared which equals this, here. We’re going to take the square root of that whole mess right here. And we’re going to take the integral of that which is this right here. And over this range 3 and 2. Y equals 2, substitute that in for the original equation here and you get thirteen twelves, add 3 substitute that in, you get 13 over 3, you take the upper minus the lower and you come up with thirteen over 4 or 3.25 units. But pretty neat, huh? everystepcalculus.com. Go to my site and hope that I make other videos for you. Have a good one.