Volume of Rotated Function: Shell Method for y=1/x on [1,4]

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Homework Statement


Find the volume of the function rotated about the x-axis over the given interval:

y=1/x

on interval [1,4]

for this specific problem it says to sketch the region and express as a sum of two integrals.

Homework Equations


The Attempt at a Solution



I'm not sure why you need to express it as a sum of two integrals. Since its about the x-axis I solved so that it was x=1/y for the radius and the height would then be y therefore with the shell method it would be 2*pi* \int (1/y)y(dy) the limits of integration being 1 to 4
 
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Shells means integrating 2*pi*r*l where r is the radius of the shell and l is the length of the shell. There are two regions of integration because between y=1/4 and y=1 the radius is y and the length depends on y (but it's not what you wrote). Between y=0 and y=1/4 the length of the shell is constant and equal to 3. If you sketched the region (and you should) I would suggest using that sketch.
 
Ohhhh, okay I get what your saying about the the 2 shells I see on the graph now as well, however I am confused about how to find what the radius is in terms of y I thought you just solved the original equation so that it was x= ??
 

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