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g Suppose that R is the finite region bounded by y = x , y = x + 4 , x = 0 , and x = 5 . Find the exact value of the volume of the object we obtain when rotating R about the x -axis.

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xero099

The volume of the solid of revolution when rotating about the x-axis is [tex]80\pi[/tex] cubic units.

How determine the volume of a solid of revolution

The volume of the solid of revolution generated by rotating about the x-axis is described by this integral formula:

[tex]V = \pi \int\limits^5_0 {[f(x)-g(x)]^{2}} \, dx[/tex] (1)

Where:

  • [tex]f(x)[/tex] - Lower function
  • [tex]g(x)[/tex] - Upper function

If we know that [tex]f(x) = x + 4[/tex] and [tex]g(x) = x[/tex], then the volume of the solid of revolution is:

[tex]V = 16\pi \int\limits^{5}_{0}\, dx[/tex]

[tex]V = 80\pi[/tex]

The volume of the solid of revolution when rotating about the x-axis is [tex]80\pi[/tex] cubic units. [tex]\blacksquare[/tex]

To learn more on solids of revolution, we kindly invite to check this verified question: https://brainly.com/question/338504

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