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This video explains how to solve integrals using the disc and annulus methods. The author provides an example of how to do this, and then discusses the theorem that states that two continuous functions that are bounded within a closed interval give rise to a region that is added to their graph. He then discusses how to rotate a region around a given line, and shows how to calculate the volume of a rotating solid formed by rotating this region around the line. Finally, the author demonstrates how to find the volume of a solid generated by revolving a region around a given line, using an example.

**00:00:00**In this video, we are going to be discussing the calculation of volumes of specific objects, specifically the method of the disco. We will start this lesson by solving a problem from earlier in the semester - Saturn, Saturno, is the least esféric of the nine planets in our solar system. It has a radial equatorial radius of 60,268 kilometers and a polar radius of 54,364 kilometers. You can see this clearly in the Voyager 1 image of Saturn taken in 1977. We will then calculate the volume of Saturn by knowing its equation of section Transversal that passes through the polar region. Therefore, at the end of this video, you will be able to solve this problem. The topic of this video is the disc method, which is a simplified version of the method of the annulus. The disc method has a continuous function in the closed interval from 9 to r. The region enclosed by this function, the axis x, and vertical lines from the origin to the point are shown. The volume of sound generated by revolving this region around the axis x comes to be good health given by the following image. Note that this is our function from the origin to here. We will rotate it around x axis to get**00:05:00**The author demonstrates how to solve integral equations by using the disco and annulus method, which is a simple and fast method. He provides an example of how to do this, and then discusses the theorem that states that two continuous functions that are bounded within a closed interval give rise to a region that is added to their graph. He then discusses how to rotate a region around a given line, and shows how to calculate the volume of a rotating solid formed by rotating this region around the line. Finally, the author demonstrates how to find the volume of a solid generated by revolving a region around a given line, using an example.**00:10:00**In this video, the different methods for solving integrals are covered. The first method is the method of disks, which is used for a function that is rotated or turned around its x-axis. After understanding the last theorem, we realize that we can rotate the function around any straight line. The second method is the method of rings, which forms a circle when two functions are combined. The last theorem is the most important, as it allows us to solve integrals involving two functions even if the line is arbitrary. Thanks for watching!

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