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Each integral represents the volume of a solid. Describe the solid.

$ \displaystyle \int_{0}^3 2 \pi x^5 dx $

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01:39

Wen Zheng

Calculus 2 / BC

Chapter 6

Applications of Integration

Section 3

Volumes by Cylindrical Shells

Campbell University

Harvey Mudd College

Idaho State University

Boston College

Lectures

00:54

Each integral represents t…

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01:44

02:00

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02:50

Okay, Describe the solid. We know that we are given from 0 to 3 to Pi X to the fifth DX. We know that this is the same thing as from 03 to pie axe Times X to the fourth D X, which is equivalent to from 0 to 3 to pie axe. Why deep water if why is extra fourth what this means? That that is the volume of the solid obtained when we rotate around the why access of wise X to the forth between zero and three, which are bounds.

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