January 10.pdf - MAT1322E C ALCULUS II E LIZABETH M ALTAIS...

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MAT1322E C ALCULUS II E LIZABETH M ALTAIS 2. Areas (Jan. 10) We know that R b a f ( x ) dx represents the net area between f , the x -axis, and the lines x = a , x = b . What if we want to know the area of a region that lies between two functions y = f ( x ) and y = g ( x ) on a given interval? A REAS B ETWEEN C URVES These notes are solely for the personal use of students registered in MAT1322. 1 what is the area Aoftphe region that lies between y=fCx ) and y=g(x ) online interval [ aid ^ A- y=fCx ) First , let's assume fk ) > gk ) > Ooh [ qb ] < - 's 's " A b v In this case , it's easy to see that it's equal to the area between the area between n' gnagjhexaxis ) - n' gnagjhexaxis ^ ^ - y=fCx ) - y=fCx ) < - y=gH < - y=gW A b A b A = Sabfk )dx - Sabgkldx =fhfH-gKDdx Now , whatiffandlorgliebelowthexaxisatsomepointtsjonf ,b] ? ^ < A- ' × ' ' ftp.yg#,ulnaAfy!gEY ' ' %Af.gg#aa-y=gKl - v •owe could break Aupintoregionsbdowlabovexaxisanduse Our Knowledge of netareas and definite integrals to figure itout . But wait !

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