Fill curve betwen specified abscissa points

Question

I am plotting the Maxwell-Boltzman distribution of molecular speeds. I want to be able to select a region to integrate using a manipulate function. Then I want to have that same region filled in on the plot. How can this be done? I can't seem to get filling to work quite correctly.

f[u_] := 
  4 Pi ( (m)/(2 Pi kb T))^(3/2) u^2 Exp[ -(m u^2)/(2 kb T)];
subs = { kb -> 1.3806 * 10^(-23), T -> 300, m -> .0032/(6*10^(23))};
Plot[f[u] /. subs , {u, 0, 5000}, 
  PlotRange -> All, 
  Filling -> {1000 -> Axis}]
Integrate[f[u] /. subs, {u, 1000, 2000}]

Manipulate[ 
 Integrate[f[u] /. subs, 
 {u, a, b}], 
 {a, 0, 5000}, 
 {b, 0, 5000} ]

This question is somewhat related. – m_goldberg Oct 10 '14 at 03:08 — m_goldberg, Oct 10 '14 at 03:08

score 4 · Answer 1 · edited Apr 13 '17 at 12:55

4

I am guessing you want to do something like

Manipulate[
 Column[{Row[{With[{a = a, b = b}, HoldForm[Integrate[f[u] /. subs, {u, a, b}]]], 
             Integrate[f[u] /. subs, {u, a, b}]}, "  =  "], 
             Plot[{ConditionalExpression[f[u] /. subs, a <= u <= b], f[u] /. subs}, 
             {u, 0, 5000}, PlotRange -> All, 
             Filling -> {1 -> Axis}, ImageSize -> 400]}],
 {a, 0, 5000}, {b, 0, 5000}]

Note: You can also use

Piecewise[{{f[u], a <= u <= b}}, Indeterminate] /. subs

or

Boole[a <= u <= b] f[u]/.subs

instead of ConditionalExpression[f[u] /. subs, a <= u <= b].

enter image description here

See also: this answer to a related Q/A

edited Apr 13 '17 at 12:55

Community

1

answered Oct 10 '14 at 00:52

kglr

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kguler I think that this question is a duplicate of the one you link with See also: -- do you disagree, and if so, why? – Mr.Wizard Oct 18 '14 at 18:17
@Mr.Wizard, it looks so.. – kglr Oct 18 '14 at 18:49

score 4 · Accepted Answer · answered Oct 10 '14 at 09:55

you can also try UnitStep

Manipulate[
 Plot[{f[u] /. subs, 
   f[u] UnitStep[u - a] UnitStep[b - u] /. subs}, {u, 0, 5000}, 
  PlotRange -> All, Filling -> {2 -> Axis}, 
  Epilog -> {PointSize[Large], 
    Point[{{a, f[a] /. subs}, {b, f[b] /. subs}}]}] , {a, 0, 
  4000}, {b, 100, 4000}]

enter image description here

Fill curve betwen specified abscissa points

2 Answers2

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