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# How to find and plot the volume of cross sections?

Posted 9 years ago
 If fx= -0.00000086x^4+0.00012x^3-0.00466x^2+0.1463x-12.18156 and gx= -0.000000000005x^6 - 0.000000004x^5 + 0.0000009x^4 - 0.0001x^3 + 0.0078x^2 - 0.3838x + 13.299 How do I find the volume of a semi-circular cross section between these two curves? Please plot it also
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Posted 9 years ago
 Very nice! I neglected to go to larger negative values.
Posted 9 years ago
 Both Wolfram Alpha and Mathematica suggest that there is a finite area between the intersections. fx = -0.00000086 x^4 + 0.00012 x^3 - 0.00466 x^2 + 0.1463 x - 12.18156; gx = -0.000000000005 x^6 - 0.000000004 x^5 + 0.0000009 x^4 - 0.0001 x^3 + 0.0078 x^2 - 0.3838 x + 13.299 We can calculate the intersections: intersecs = NSolve[{fx == gx, x \[Element] Reals}, x] (*{{x -> -1143.28}, {x -> 167.48}}*) We can now integrate: Integrate[gx - fx, {x, x /. intersecs[], x /. intersecs[]}] (*4.53217*10^8*) Here is the plot that looks just like the one that Wolfram Alpha produces: Plot[{gx, fx}, {x, x /. intersecs[], x /. intersecs[]}, Filling -> { 1 -> {2}}, PlotRange -> All] Cheers,Marco
Posted 9 years ago
 It is useful to first make a plot of the two functions: Plot[{-0.00000086 x^4 + 0.00012 x^3 - 0.00466 x^2 + 0.1463 x - 12.18156, -0.000000000005 x^6 - 0.000000004 x^5 + 0.0000009 x^4 - 0.0001 x^3 + 0.0078 x^2 - 0.3838 x + 13.299}, {x, -200, 500}] You will see that there doesn't appear to be any finite area between intersections.
Posted 9 years ago
 http://www.wolframalpha.com/input/?i=area+between++-0.00000086x%5E4%2B0.00012x%5E3-0.00466x%5E2%2B0.1463x-12.18156+and++-0.000000000005x%5E6+-+0.000000004x%5E5+%2B+0.0000009x%5E4+-+0.0001x%5E3+%2B+0.0078x%5E2+-+0.3838x+%2B+13.299You may need to change the endpoints of the integration. Are you using Mathematic or Wolfram|Alpha?