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