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
You may need to change the endpoints of the integration. Are you using Mathematic or Wolfram|Alpha?
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.
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[[1]], x /. intersecs[[2]]}]
(*4.53217*10^8*)
Here is the plot that looks just like the one that Wolfram Alpha produces:
Plot[{gx, fx}, {x, x /. intersecs[[1]], x /. intersecs[[2]]}, Filling -> { 1 -> {2}}, PlotRange -> All]
Cheers,
Marco
Very nice! I neglected to go to larger negative values.
