Solution
Given the function
[tex]f(x)=(3x+5)^3[/tex]If we graph the equation, we would have.
when x = 0, f(x) = 5^3 = 125
when x = 1, f(x) = 8^3 = 512
Hence, the solid of revolution is given by
[tex]V=\pi\int_0^1(3x+5)^6dx[/tex]Evaluating the integral
[tex]\begin{gathered} V=\frac{\pi}{7\times3}[(3x+5)^7]\text{ from 0 to 1} \\ \\ \end{gathered}[/tex][tex]\Rightarrow V=\frac{\pi}{21}(8^7-5^7)\text{ unit}^3[/tex]
