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Finding the volume of a solid of revolution (washer method) Using the washer method, determine the volume of a solid formed by revolving the region bounded by the line y = x and the curve y = 1/x from x = 1 to x = 4 about the x-axis. The 2d picture below may help in determining the inner and outer radius of the washer used in setting up the integral for the volume. For a dynamic 3d look at the solid, click here (This will open a new window.) Part 1. Setup the integral that represents the volume of the solid of revolution described above.. Part 2. The volume of the solid is units cubed. 

          Finding the volume of a solid of revolution (washer method)
Using the washer method, determine the volume of a solid formed by revolving the region bounded by the line y = x and the curve y = 1/x from x = 1 to x = 4 about the x-axis.
The 2d picture below may help in determining the inner and outer radius of the washer used in setting up the integral for the volume.
For a dynamic 3d look at the solid, click here
(This will open a new window.)
Part 1.
Setup the integral that represents the volume of the solid of revolution described above..
Part 2.
The volume of the solid is units cubed.
Show more…
Finding the volume of a solid of revolution (washer method) Using the washer method, determine the volume of a solid formed by revolving the region bounded by the line y = x and the curve y = 1/x from x = 1 to x = 4 about the x-axis. The 2d picture below may help in determining the inner and outer radius of the washer used in setting up the integral for the volume. For a dynamic 3d look at the solid, click here (This will open a new window.) Part 1. Setup the integral that represents the volume of the solid of revolution described above.. Part 2. The volume of the solid is units cubed.

Added by Jocelyn E.

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Calculus: Early Transcendentals
Calculus: Early Transcendentals
James Stewart 8th Edition
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Finding the volume of a solid of revolution (washer method) Using the washer method, determine the volume of a solid formed by revolving the region bounded by the line y = x and the curve y = 1/x from x = 1 to x = 4 about the x-axis. The 2d picture below may help in determining the inner and outer radius of the washer used in setting up the integral for the volume. For a dynamic 3d look at the solid, click here (This will open a new window.) Part 1. Setup the integral that represents the volume of the solid of revolution described above.. Part 2. The volume of the solid is units cubed.
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Transcript

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00:02 Get you this answer, but i'm not exactly sure what the blanks are for, because if i'm looking at from x equals 1 to x equals 4, you know, is their first intention getting you to realize what that volume would be? because if you do the disk method for that only, it would just be pi, the integral from 1 to 4 of that function being squared.
00:28 But that's not right.
00:30 Because then you have to take the other function.
00:32 Let me double check, which is 1 over x, which i would actually rewrite as x to the negative first.
00:40 Because you have to find that area now revolved.
00:45 I'll give you a little nicer picture.
00:47 And so you can see that you have to subtract.
00:51 So that's why with the washer method, we usually just put it all together pi.
00:59 So maybe their first blank is to have, in front and then the integral from 1 to 4 of well i don't like how i circled pi so 1 to 4 of the upper function squared minus the lower function squared d x and you might as well take it a step further and just rewrite it because a power to a power you multiply those exponents and at this point you just have to add one to your exponent and multiply by the reciprocal of your new exponent.
01:36 Now, adding 1 to negative 2 is negative 1, if you multiply by the reciprocal, you get positive 1, going from 1 to 4...
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