1322e-20191-notes02-filled-1.pdf - MAT1322 C ALCULUS II E...

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MAT1322 CALCULUSIIELIZABETHMALTAIS2. AreasWe know thatRbaf(x)dxrepresents the net area betweenf, thex-axis, and the linesx=a,x=b.What if we want to know the area of a region that lies between two functionsy=f(x)andy=g(x)on a given interval?AREASBETWEENCURVESThese notes are solely for the personal use of students registered in MAT1322.1whatistheareaAoftpheregionthatliesbetweeny=fCx)andy=g(x)onlineinterval[aid^A-y=fCx)First,let'sassumefk)>gk)>Ooh[qb]<-='s"AbvInthiscase,it'seasytoseethatit'sequaltotheareabetweentheareabetweenn'gnagjhexaxis)-n'gnagjhexaxis^^-y=fCx)-y=fCx)<-Y=gH<-y=gWAbAbA=Sabfkjdx-Sabgkldx=fhfH-gKDdxNow,whatiffandlorgliebelowthexaxisatsomepointtsjonf,b]?^<A-'×''|aAb#y=yg¥,u<÷tn~!gYI"'%Af.gg#aa-y=gKl-v•owecouldbreakAupintoregionsbdowlabovexaxisanduseOurKnowledgeofnetareasanddefiniteintegralstofigureitout.Butwait!Nothingabouttheregionitselfhaschanged.

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