Volumes Q (1 Viewer)
- Thread starter girrawhat
- Start date
RobertHannah89
New Member
- Joined
- Jul 1, 2012
- Messages
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- Male
- HSC
- 2007
Hi there!
Perhaps the best way to start a question like this is to see if you can picture the graph of the functions in your head (or draw them). This will give you a better idea of what's going on. If you can't, use this function plotter: http://www.univie.ac.at/future.media/moe/fplotter/fplotter.html
Ok. So picture in your head the shells. We're rotating about the line
, so clearly these shells are going to have a radius of 
.
In the region
, we know that 
is going to be larger than 
(because the second function is negative!).
Therefore, the height of these shells is
.
And that's it! The volume of the little shells going to be:
|x-2|dx)
Hence the volume is just
(2-x)dx)
Why
? Because in the region of integration, 
.
Hope this helps!
Rob
Perhaps the best way to start a question like this is to see if you can picture the graph of the functions in your head (or draw them). This will give you a better idea of what's going on. If you can't, use this function plotter: http://www.univie.ac.at/future.media/moe/fplotter/fplotter.html
Ok. So picture in your head the shells. We're rotating about the line
In the region
Therefore, the height of these shells is
And that's it! The volume of the little shells going to be:
Hence the volume is just
Why
Hope this helps!
Rob
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