So it's really important to keep in mind with the Y. This is going to be important when you're deciding if you need DX dy y, and then how to take the derivatives of each of these. Keep in mind, though, d y if you have D Y, that means you have an ex equals equation, and if you have DX, that means you have a Y equals equation. So keep that in mind that it's explained more than surface area video, and it comes pretty naturally which equation to use. A bunch of stuff also in here has to be changed. So DX or do I d x t x t y squared DX surface area can be used or D y if you change it to D y. This time we have to pie y where why is the equation of the curve times the square root of one plus the derivative of the curve. It's gonna be represented with an s equal to again the integral from A to B. Exercises 47 and 48, use the integration capabilities of a graphing utility to approximate the surface area of the solid of revolution. So that's the basic concept behind surface area and the formula that we're going to be using for surface area. Um, if you ever have a piece of construction paper, regular paper and it's a rectangle, but then you fold it together and it makes a cylinder and unfold it back to the piece of paper. So if you can picture a rectangle, this is how we find the surface area. So if you can picture a square, a rectangle and that a rectangle is what a cylinder is unraveled. We don't just find the area, but we unravel this and make it flat. So in three D, try and picture this, and we want to know the surface area of it to find the surface area. So if we have a some kind of fear or cone like saying that maybe looks like this. So basically, surface area is if you have a shape and you unravel it. They are very related, which we will talk a lot about in the lecture video for surface area. So we're also going to be talking about surface area. But okay, so this is what we're going to be doing with our blank and then the other part of this next topic is surface area. And the equation that we have for our Klink is going to be that the length of the curve is equal to the integral from a to B of the square root of one, plus the derivative of the function, the the derivative of this function squared and then deep s eso again, a reminder the notation D y dx, this is a derivative you're in. In rectangular coordinates, the arc length of a. We're gonna approximate the length of the curve using integration. Arc length is the distance between two points along a section of a curve. So let's say we have this and the formula for arc length. And I explained this formula a bit more in detail in the lecture videos. So our Klink is basically when you have a curve and you want to find the length of this curb eso the curve could be, Let's say it's an ffx function. So the next topics we're going to cover our art link.
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