Filling between boundaries

Question

I would like to visualize what it graphically means to integrate between two boundary values. Therefore I'd like to make a Filling between these two values. Is there a way to get this done?

kglr · Accepted Answer

An alternative is to use Piecewise as follows Plot[{Sin[x], Piecewise[{{Sin[x], -Pi <= x <= Pi}}, _]}, {x, -2 Pi, 2 Pi}, Filling -> {2 -> {Axis, Yellow}}, PlotStyle -> {Green, Directive[Red, Thick]}] which gives Or Use Show to superimpose two variants (the second one with your choice of the variable bounds -- -Pi and 2Pi in the example below) of the plot: Show[Plot[Sin[x], {x, -3 Pi, 3 Pi}], Plot[Sin[x], {x, - Pi, 2 Pi}, Filling -> Axis, FillingStyle -> Yellow]] Update: Yet another method using ColorFunction with ColorFunctionScaling->False, Mesh and MeshShading, Plot[Sin[x], {x, -2 Pi, 2 π}, Mesh -> {{0}}, MeshShading -> {Directive@{Thick, Blue}}, Filling -> Axis, ColorFunction -> (If[-Pi <= #1 <= Pi/2, If[#2 > 0, Red, Yellow], White] &), ColorFunctionScaling -> False] Update 2: All inside Manipulate: First, a cool combo control from somewhere in the docs: popupField[Dynamic[var_], list_List] := Grid[{{PopupMenu[Dynamic[var], list, 0, Opener[False, Appearance -> Medium]], InputField[Dynamic[var], Appearance -> "Frameless"]}}, Frame -> All, FrameStyle -> Orange, Background -> {{Orange, Orange}}] and, then, Manipulate[Column[{ Dynamic@Show[ Plot[func[x], {x, -2 Pi, 2 π}, Ticks -> {Range[-2 Pi, 2 Pi, Pi/2], Automatic}, Mesh -> {{0}}, MeshShading -> {Directive@{Thick, color0}}, Filling -> Axis, ColorFunction -> (If[lb <= #1 <= ub, If[#2 > 0, color1, color2], White] &), ColorFunctionScaling -> False, ImageSize -> {600, 300}], Graphics[{Gray, Line[{{-2 Pi, 0}, {2 Pi, 0}}], Orange, PointSize[.02], Dynamic[(Point[{lb = Min[First[pt1], First[pt2]], 0}])], Brown, PointSize[.02], Dynamic[(Point[{ub = Max[First[pt1], First[pt2]], 0}])]}, PlotRange -> 1.], PlotLabel -> Style[ "nArea = " <> ToString[Quiet@NIntegrate[func[t], {t, lb, ub}]] <> "n", "Subsection", GrayLevel[.3]]]}, Center], Row[{Spacer[30], Rotate[Style["functions", GrayLevel[.3], 12], 90 Degree], Spacer[5],Control@{{func, Sin, ""}, popupField[#, {Sin, Cos, Sec, Cosh, ArcSinh}] &} Spacer[15], Rotate[Style["colors", GrayLevel[.3], 12], 90 Degree], Spacer[5], Rotate[Style["line", GrayLevel[.3], 10], 90 Degree], Control@{{color0, Blue, ""}, ColorSlider[#, AppearanceElements -> "Spectrum", ImageSize -> {40, 40}, AutoAction -> True] &}, Spacer[5], Rotate[Style["above", GrayLevel[.3], 10], 90 Degree], Control@{{color1, Green, ""}, ColorSlider[#, AppearanceElements -> "Spectrum", ImageSize -> {40, 40}, AutoAction -> True] &}, Spacer[5], Rotate[Style["below", GrayLevel[.3], 10], 90 Degree], Control@{{color2, Green, ""}, ColorSlider[#, AppearanceElements -> "Spectrum", ImageSize -> {40, 40}, AutoAction -> True] &}},Spacer[0]], {{lb, -Pi}, ControlType -> None}, {{ub, 3 Pi/2}, ControlType -> None}, {{pt1, {-Pi, 0}}, Locator, Appearance -> None}, {{pt2, {3 Pi/2, 0}}, Locator, Appearance -> None}, Alignment -> Center, ControlPlacement -> Top, AppearanceElements -> Automatic] Enter your own pure function:

jVincent · Answer

Always search the doc when you don't know what to do. In most cases you'll not only find it possible, but find a thorough documentation along with examples. In this case you have this link.

Here is an example:

Show[
 Plot[{Cos[x], Sin[x]}, {x, 0, 2 π}],
 Plot[{Cos[x], Sin[x]}, {x, π/4, 5/4 π}, 
     PlotRange -> {{0, 2 π}, All} , Filling -> 1 -> {2}]
]

Vitaliy Kaurov · Answer

Area will be red or blue depending whether $b > a$ or not.
Manipulate[
  Plot[{f[x], UnitStep[Sign[b - a] (x - a)] UnitStep[Sign[b - a] (b - x)] f[x]}, 
    {x, -7, 7}, PlotStyle -> {Thick, Thickness[0]}, Filling -> {2 -> 0}, 
  FillingStyle -> Directive[Opacity[.5], If[b - a > 0, Red, Blue]], 
  PlotLabel -> "AREA = " <> ToString[NIntegrate[f[x], {x, a, b}]]], {{b, 4}, -7, 7},   
   {{a, -1}, -7, 7}, {f, {Sin, Cos, Tanh, Sech}}]

Also take a look at source code at the Wolfram Demonstration Project.

Dr. belisarius · Answer

With axis-constrained locators: DynamicModule[{pts = {{0, 0}, {Pi, 0}}}, LocatorPane[Dynamic[pts, (pts[[1]] = {#[[1, 1]], 0}; pts[[2]] = {#[[2, 1]], 0}) &], Dynamic[ Framed@Show@ {Plot[Sin@x, {x, 0, 2 Pi}], Plot[Sin@x, {x, pts[[1, 1]], pts[[2, 1]]}, Filling -> Axis] } ]]] Edit This is the full code, with the label: DynamicModule[{pts = {{0, 0}, {Pi, 0}}}, LocatorPane[Dynamic[pts, (pts[[1]] = {#[[1, 1]], 0}; pts[[2]] = {#[[2, 1]], 0}) &], Dynamic[ Framed@Show@ {Plot[Sin@x, {x, 0, 2 Pi}, PlotLabel -> ToString@StandardForm[Integrate[sin[x], {x, pts[[1, 1]], pts[[2, 1]]}]] <> " = " <> ToString[Integrate[Sin@x, {x, pts[[1, 1]], pts[[2, 1]]}]]], Plot[Sin@x, {x, pts[[1, 1]], pts[[2, 1]]}, Filling -> Axis] } ]]]

nielses · Answer

I made an answer by J.M. and Murta into a function:

IntegralPlot[f_, {x_, L_, U_}, {l_, u_}, opts : OptionsPattern[]] := 
 Module[{col = ColorData[1, 1]},
  Plot[{ConditionalExpression[f, x > l && x < u], f},
   {x, L, U},
   Prolog -> {{col, Line[{{l, 0}, {l, f /. {x -> l}}}]}, {col, 
      Line[{{u, 0}, {u, f /. {x -> u}}}]}},
   Filling -> {1 -> Axis},
   PlotStyle -> col,
   opts]]

IntegralPlot[PDF[NormalDistribution[0, 1]][x], {x, -4, 4}, {1, 2}]

IntegralPlot[x^2, {x, 0, 10}, {4, 6}, PlotLabel -> "x^2"]

Mats Granvik · Answer

Copying the second code snippet of user kglr's answer I changed the command Filling->Axis into Filling->0.

(*start*)
integrationLimit1 = 1;
integrationLimit2 = 8;
f[x_] = 100 - 8*x^2 + x^3;
g1 = Plot[f[x], {x, -5, 10}];
g2 = Plot[f[x], {x, integrationLimit1, integrationLimit2}, 
   Filling -> 0];
Show[g1, g2]
(*end*)

Also, the order of the graphics g1 and g2 in the Show command are important.

Filling between boundaries

6 Answers

Add your own answers!

Ask a Question