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Volumes by Rotations

Volumes by Rotations. Using the disk and shell method. By revolving a function around an axis, you generate a solid of revolution. Calculus allows us to find the volume of the rotation using definite integration. You need to first take out a cross section or “disc” from the solid.

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Volumes by Rotations

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  1. Volumes by Rotations Using the disk and shell method

  2. By revolving a function around an axis, you generate a solid of revolution.

  3. Calculus allows us to find the volume of the rotation using definite integration. You need to first take out a cross section or “disc” from the solid. What is the radius of the disc? What is the area of the face of the disc? The width of the disc? The volume of the disc? How do you add up all the possible discs? dx r

  4. When a region is revolved about a line which is not one of its boundaries, its volume is formed from a sum of volumes of washers (discs with holes in them). f(x) g(x)

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