Question

Using disks or washers, find the volume of the solid obtained by rotating the region bounded by the curves y=1/x, y=0, x=1, and x=4 about the line y=−1.

Answer 1

`(3)/(4)\pi +4\pi\ln2`

Explanation:

`y = (1)/(x) ,\:\:y=0,\:\:x=1,\:\:x=4`

about the line y = -1

`V=\pi\int\limits^4_1[((1)/(x)+1)^2-(0+1)^2]\:dx=\pi\int\limits^4_1((1)/(x^2)+(2)/(x)+1-1)\:dx=\\\\=\pi(-(1)/(x)+2\ln x)|^4_1=\pi(-(1)/(4) +2\ln 4+1-2\ln 1)=(3)/(4)\pi +4\pi\ln2`