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7.2 Volume: The Disc Method PowerPoint Presentation
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7.2 Volume: The Disc Method

7.2 Volume: The Disc Method

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7.2 Volume: The Disc Method

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  1. 7.2 Volume: The Disc Method The area under a curve is the summation of an infinite number of rectangles. If we take this rectangle and revolve it about a line, we have a disc.

  2. This disc is nothing more than a cylinder on it’s side. r The volume of a cylinder is: Disc If we sum up an infinite number of cylinders, we have the new integration formula: r = h & w = dx This equation is for a horizontal axis of revolution.

  3. Vertical axis of revolution

  4. Ex. y = x2, y = 0, and x = 2 about the x-axis r = y

  5. Ex. y = x2, x = 0, and y = 4 about the y-axis r = x

  6. Find the radius for y = x2, y = 0, and x = 2 about the line x = 2 about the line x = 3 4 4 2 x r = 2 - x x = 3