How would you find the volume of a solid rotating about y-axis if you were not given f(x)?, or better yet, how would you come up with the equation of f(x)?

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- Feb 29th 2008, 09:34 AMch2kb0xvolume of solid without f(x)
How would you find the volume of a solid rotating about y-axis if you were not given f(x)?, or better yet, how would you come up with the equation of f(x)?

- Feb 29th 2008, 09:56 AMgalactus
You could use various points(x and y coordinates)and implement the proper regression analysis to find an equation. Then revolve.

There are linear regressions, cubic regressions, quartic and quintic regressions, exponential, etc.

A lot of the calculators do these analyses.

For example, suppose we had x values, respectively, of 0,1,2,3,4

y values of 0,2,5,7,11

I ran these through my calculator and got an equation of

$\displaystyle y=\frac{5}{24}x^{4}-\frac{19}{12}x^{3}+\frac{91}{24}x^{2}-\frac{5}{12}x$

Hope this helps a little. - Feb 29th 2008, 10:12 AMch2kb0x
ohh ok,

how would I enter values into my TI-83 to find an equation?

or does it only work with TI-89

I mean, I know how to plot the data, but i'm not sure if TI-83 is capable of producing an equation.

If not, how would I derive an equation based on the x,y values? - Feb 29th 2008, 10:59 AMgalactus
You need some sort of tech to derive the equation. Even a simple linear regression is rather cumbersome, let alone anything higher. I don't know if an 83 will do it or not. I use a Voyage 200 and a TI-92. They certainly do. The 89 will. If you have Excel, it will do it.

If you can gain access to an 89 or Excel, let me know and I can show you the steps. - Feb 29th 2008, 11:20 AMearboth
- Feb 29th 2008, 11:27 AMgalactus
There ya' go. I wasn't sure if an 83 would or not. Now we know. That is exactly what my Voyage 200 gave me except I converted to fractions to make it look better.

- Feb 29th 2008, 05:03 PMch2kb0x
thank you so much, both of you. thanks.