When finding the volume of a solid, how do you know which method to use? How do you conclude if disk/washer or cylindrical shells method is better? Explain

Calculus: Early Transcendentals
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Author:James Stewart
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Chapter1: Functions And Models
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When finding the volume of a solid, how do you know which method to use? How do you conclude if disk/washer or cylindrical shells method is better? Explain

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Use washers when you've been given two equations.

For example, if we've got y=x and y=x^2, and we wanted to find the volume of the solid when rotated around the x-axis, we would view this shape as made of washers.

If we've only been given a single curve--y=x, for example--we imagine the solid rotated around the x-axis and realize it's a cylinder. A washer has holes in it, so it's not particularly helpful here--we'll use disks.

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