Volume of Revolution = [tex] \pi \int\limits^b_a {y^{2}} \, dx [/tex]
Volume of Revolution = [tex] \pi \int\limits^3_1 { (\frac{5}{x})^{2}} \, dx[/tex]
= [tex]\pi \int\limits^3_1 ({\frac{25}{x^{2}}) \, dx[/tex]
= [tex]25\pi \int\limits^3_1 ({\frac{1}{x^{2}}) \, dx[/tex]
= [tex]25\pi \int\limits^3_1 ({x^{-2}}) \, dx[/tex]
= [tex]25\pi \ ^{3} [-x^{-1}] _{1}
[/tex]
[tex]= 25\pi\ ((-1/3) - (-1/1)) \\
= 25\pi\ (2/3) \\
= 50/3 \pi\ units^{3} [/tex]
