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Ln(x) rotated around the xaxis [1,4] Find Volume 
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#1
Jan2708, 06:48 PM

P: 1

1. The problem statement, all variables and given/known data
The function ln(x) is rotated around the xaxis on the interval [1,4]. 2. Relevant equations Find the volume of the figure using integration. 3. The attempt at a solution [tex]\pi[/tex] [tex]\int _{1}^{4} (.75) ln(x)^{2} dx[/tex] = [tex]\pi[/tex] [tex]\int _{1}^{4} [3(ln(x))^{2}]/4 [/tex] 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 


#2
Jan2708, 07:20 PM

HW Helper
P: 6,207

try letting
u=lnx and then go from there 


#3
Jan2708, 09:19 PM

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 cylindricalish 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: [tex]dV = \pi*r^2 dx[/tex] One problem though. The radius of these slabs is constantly changing according to ln(x) [tex]dV = \pi(lnx)^2 dx[/tex] [tex]V = \int _{1}^{4} \pi(lnx)^2 dx[/tex] is what I'm getting? 


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