6.2a DISKS METHOD (SOLIDS OF REVOLUTION)

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Presentation transcript:

6.2a DISKS METHOD (SOLIDS OF REVOLUTION) Rita Korsunsky

Separate the area into rectangles of equal length Let’s revolve region under f(x) from a to b about x- axis Revolve each separately to form many disks Total volume =sum of volumes of infinitely thin individual disks

Disk Method a b d c

Example. The region bounded by the graph of y = x2 + 1, the x-axis, and the lines x = - 1 and x = 1 is revolved about the x axis. Find the volume of the resulting solid. 1. Graph the Region and identify the thickness (dx or dy) 3.) Integrate 2.) Express the radius for one disk in terms of x (if dx) or y (if dy)

Example. The region bounded by the y-axis and the graphs of y=x3, y=1, and y=8 is revolved about the y-axis. Find the volume of the resulting solid. Volume of Resulting Solid: 58.4

Example: Sketch the region R bounded by the graphs of and from 0 to , and find the volume of the solid generated if R is revolved about the x- axis. 1 -1