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In summary, the conversation discusses the correct setup for an integral involving horizontal disks and the use of shells instead of washers. It is recommended to use two integrals, one from 0 to 1/2 and the other from 1/2 to 1, to find the total area. The previous incorrect integral is also mentioned.

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- #2

Mark44

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That is incorrect, because your integral is not set up correctly. You are using horizontal disks (washers), but because of the shape of the region, their formula needs to change at y = 1/2. Between 0 and 1/2, the washers have the same outside diameter. Between 1/2 and 1, the washers have a different outside diameter. Since the formulas are different, you will need two integrals.saruji said:The file is a PDF, but here is an imgur link, anyone?

I would probably be inclined to use shells rather than washers in this problem.

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saruji

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- #4

iRaid

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Lol, I had this exact same problem on my quiz last week and got it wrong. I figured it out after class (while driving home, unfortunately) and what you have to do is set up 2 integrals. One from 0 to 1/2 and the other from 1/2 to 1. Adding these together gives you the total area.

[tex]\pi\int_0^.5 (outer)^{2}-(inner)^{2} dy + \pi\int_.5^1 (outer)^{2}-(inner)^{2} dy[/tex]

That should make it much easier.

Edit: Just to add, you can tell yours is wrong when you go to evaluate it, what's ln 0? undefined..

[tex]\pi\int_0^.5 (outer)^{2}-(inner)^{2} dy + \pi\int_.5^1 (outer)^{2}-(inner)^{2} dy[/tex]

That should make it much easier.

Edit: Just to add, you can tell yours is wrong when you go to evaluate it, what's ln 0? undefined..

Last edited:

- #5

saruji

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iRaid said:

[tex]\pi\int_0^.5 (outer)^{2}-(inner)^{2} dy + \pi\int_.5^1 (outer)^{2}-(inner)^{2} dy[/tex]

That should make it much easier.

Edit: Just to add, you can tell yours is wrong when you go to evaluate it, what's ln 0? undefined..

Thank you so much

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The volume of a solid of solids can be calculated by finding the volume of each individual solid shape and then adding them together.

A solid of solids is a specific type of composite solid where the individual shapes are combined to create one larger shape. A composite solid can refer to any combination of solid shapes.

The formula for finding the surface area of a solid of solids depends on the specific shapes that make up the solid. Generally, the surface area can be found by adding the surface areas of each individual shape.

Yes, a solid of solids can have curved edges if the individual shapes that make up the solid have curved edges. For example, a solid of solids made up of spheres and cylinders can have curved edges.

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