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)?
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.
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?
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.