# Ln(x) rotated around the x-axis [1,4] Find Volume

by natemac42
Tags: rotated, volume, xaxis
 P: 1 1. The problem statement, all variables and given/known data The function ln(x) is rotated around the x-axis on the interval [1,4]. 2. Relevant equations Find the volume of the figure using integration. 3. The attempt at a solution $$\pi$$ $$\int _{1}^{4} (.75) ln(x)^{2} dx$$ = $$\pi$$ $$\int _{1}^{4} [3(ln(x))^{2}]/4$$ sorry I'm bad at typing these things in anyway solving that I got 6.1187 units^3 and I don't think it's the correct answer, but I'm not sure. I approximated the volume using cylinders and got 10.518 for circumscribed and 5.989 for inscribed. Thanks in advance
 P: 1,345 We can solve this by breaking the object created by breaking it into small parts. Since we're rotating the function around an axis we'll get a cylindrical-ish object. So we can find the area of a slab of the object by multiplying the area by an infinitely small width (dx). So an infinitely small piece of the solid is the area by the width: $$dV = \pi*r^2 dx$$ One problem though. The radius of these slabs is constantly changing according to ln(x) $$dV = \pi(ln|x|)^2 dx$$ $$V = \int _{1}^{4} \pi(ln|x|)^2 dx$$ is what I'm getting?