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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

POSTED BY: Matt Jin
4 Replies

Very nice! I neglected to go to larger negative values.

POSTED BY: S M Blinder

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]

enter image description here

Cheers,

Marco

POSTED BY: Marco Thiel

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 BY: S M Blinder
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