volume of a solid using integration

[Brain0991]

A region is bounded by:

y = 10/x^2, y = 0, x = 1, x = 5

and is revolved around the given axes. Find the volume of the solid generated.

(a) x-axis
(b) y-axis
(c) line y=10

I am assuming I use the shell method

 

[BigGlenntheHeavy]

\(\displaystyle a) \ x-axis \ (disc), \ \ \pi\int_{1}^{5}\bigg(\frac{10}{x^2}\bigg)^2dx\)

\(\displaystyle b) \ y-axis \ (shell), \ 2\pi\int_{1}^{5}\bigg(\frac{10}{x^2}\bigg)xdx\)

\(\displaystyle c) \ y \ =10 \ (disc), \ \pi\int_{1}^{5}[(0-10)^2-(10/x^2-10)^2]dx\)

\(\displaystyle See \ graph\)

[attachment=0:ggbsn852]ccc.jpg[/attachment:ggbsn852]