Find the volume of the solid obtained by rotating the region-2

phillyolly
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Homework Statement


Find the volume of the solid obtained by rotating the region bounded by the given curves about the specified line. Sketch the region, the solid, and a typical disk or washer. About x axis.

y=sqrt(25-x2)
y=0
x=2
x=4

Homework Equations





The Attempt at a Solution


I drew a graph, region and solid. Please help me out with the disk.
Jump start for any solution, please?
 

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I posted this in your other thread, here's the link: https://www.physicsforums.com/showthread.php?t=418382"

This figure should give you some intuition on visualizing the disks.

I don't really understand where your confusion lies, so if there is any please specify where and why.
 
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There are two things I don't understand about this problem. First, when finding the nth root of a number, there should in theory be n solutions. However, the formula produces n+1 roots. Here is how. The first root is simply ##\left(r\right)^{\left(\frac{1}{n}\right)}##. Then you multiply this first root by n additional expressions given by the formula, as you go through k=0,1,...n-1. So you end up with n+1 roots, which cannot be correct. Let me illustrate what I mean. For this...
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