Question

Find the volume of the solid obtained by rotating the region enclosed by y=1x2,y=0,x=1, and x=8, about the line y=−3 using the method of disks or washers.

Answer 1

I assume the first equation is
`y=\frac1{x^2}`. Using the method of washers, the volume is

`\displaystyle\pi\int_1^8\left(\frac1{x^2}+3\right)^2-3^2\,\mathrm dx=\pi\int_1^8\frac1{x^4}+\frac6{x^2}\,\mathrm dx=\boxed{(8575\pi)/(1536)}`