Re: find area bounded by three linear functions

• To: mathgroup at smc.vnet.net
• Subject: [mg68368] Re: [mg68357] find area bounded by three linear functions
• From: Bob Hanlon <hanlonr at cox.net>
• Date: Thu, 3 Aug 2006 06:06:25 -0400 (EDT)
• Reply-to: hanlonr at cox.net
• Sender: owner-wri-mathgroup at wolfram.com

```Needs["Graphics`"];

InequalityPlot[{x>3y,x+y>0,7x+3y<24},
{x,-1,7},{y,-10,3},
Epilog->{
Text["x = 3 y",{1.5,0.5},{1,-1}],
Text["x + y = 0",{3,-3},{1,1}],
Text["7x + 3y = 24",{4.5,-2.5},{-1,-1}]},
PlotRange->{{-1,7},{-7,2}}];

eqns={x==3y,x+y==0,7x+3y==24};

Solve[#,{x,y}]&/@Subsets[eqns, {2}]

{{{x -> 0, y -> 0}}, {{x -> 3, y -> 1}},
{{x -> 6, y -> -6}}}

Integrate[1,{x,0,3},{y,-x,x/3}]+
Integrate[1,{x,3,6},{y,-x,(24-7x)/3}]

12

Integrate[Boole[x>3y&&x+y>0&&7x+3y<24],
{x,-Infinity,Infinity},{y,-Infinity,Infinity}]

12

Bob Hanlon

---- T Harris <tdh1967 at bellsouth.net> wrote:
> How can I get Mathematica to find the area of the region bounded by all
> three of the following linear functions?  I have tried searching and can't
> find it.  What do I search for to find the commands to accomplish this?  I
> calculated by hand and come up with about 3.1623 sq. units for area above
> the x-axis and 8.8378 sq. units below it.  The total area for the scalene
> triangle formed is 12 square units by my calculations using Heron's formula.
>
> X=3Y;  X+Y=0;   7X + 3Y =24
>
> Thanks,
>
> T Harris
>

```

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