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 >