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I have no clue how to do these types of problems on mathematica and I have no clue how to even search mathematica for help.
What do I need to do to find out how to solve these problems in mathematica?
I tried google to no avail, I guess I don't know what to look for.
Try RevolutionPlot3D:
RevolutionPlot3D[x^2, {x, 0, 1}]
That would simply rotate the half-parabola around the z-axis. Need to work with the help-function: Type that above into Mathematica, put cursor over it, press F1 and you'll get help as well as other related functions. The help is much improved in ver 6.
You mean it will revolve around the x-axis right?
I heard that mathematica has lots of examples, but I am having trouble finding them. For example, what would I type in order to find the volume of the area enclosed by y=x^2 y=2x x=2 x=4 around the y-axis? (I just made those numbers up right now, hopefully they will work, otherwise a similar example that works would be awesome)
Ok, y-axis. You have to build them up although there may be an easier way to do that. Here's what I came up with. The second is a cross-section of the volume of revolution.
Code:cyl = ParametricPlot3D[{4*Cos[t], 4*Sin[t],
z}, {t, 0, 2*Pi}, {z, 8, 16}]
p1 = RevolutionPlot3D[{x^2}, {x, 2, 4},
BoxRatios -> {1, 1, 1}, PlotStyle -> Red]
p2 = RevolutionPlot3D[{2*x}, {x, 2, 4},
BoxRatios -> {1, 1/4, 1},
PlotStyle -> Blue]
fig1 = Show[{p1, p2, cyl}]
fig2 = Show[{p1, p2, cyl}, PlotRange ->
{{-4, 4}, {0, 4}, {0, 16}}]
GraphicsArray[{{fig1, fig2}}]