# Thread: Improper Integral: Volume Around x-axis

1. ## Improper Integral: Volume Around x-axis

let f(x)=1/(0.5x+1.8), by rotating R={(x,y)/ x>=0,0<=y<=1/(0.5x+1.8)}about the x axis we obtain a solid , Calculate the volume

2. Originally Posted by shannon1111
let f(x)=1/(0.5x+1.8), by rotating R={(x,y)/ x>=0,0<=y<=1/(0.5x+1.8)}about the x axis we obtain a solid , Calculate the volume
$f(x) = \frac{2}{x+3.6}$

$V = \pi \int_0^{\infty} \left(\frac{2}{x+3.6}\right)^2 \, dx$

$V = 4\pi \lim_{b \to \infty} \int_0^b \frac{1}{(x+3.6)^2} \, dx$

$V = 4\pi \lim_{b \to \infty} \left[-\frac{1}{x+3.6}\right]_0^b$

$V = 4\pi \lim_{b \to \infty} \left[\frac{1}{3.6}-\frac{1}{b+3.6}\right] = \frac{10\pi}{9}$