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Numerade Educator

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Problem 29 Medium Difficulty

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

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

Answer

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

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Video Transcript

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.