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Approximationofefinitentegrals We cannot always evaluate the integral in the real world so we need to estimate the values his chapter explores many different rules to estimate an integration Ax fix fixa fly fixn SimpsonsRue Sironsuleshortcut ext use the midpoint rule with n 4 to Approximate ax a iii iii so 2 fify ax fixdx f0 25 f10 75 11 25tf 1 757 2s H 1 75 11 10 56469616 ex use the trapezoidal rule with n 4 to approximate f dx same as before c flxldx 12 f10 E I 2105 F 0 56925456 2 f 1 0 712 0 2 f 1 5 f a 5mg of dye is injected into a vein leading totheheart The concentration ofthedye in the orta is determined every 2 seconds for 22 seconds Let clt be the concentration in the aorta ter t seconds Use the trapezoidal rule toestimate socity dt tn 9 0 5 22 At 11 2 I 4 6 s to 12 it it is to z I 101 244 2014 2C 6 citdt I 1 0 210 2106 2114 t 262 7 23 7 2141 2 13 87 2129 2115 210 9 2C 20 122 0 5 43 7l it If youwanttoconvertthis toliters m whichwould a min A Psychologists usevarious standardized tests tomeasureintelligenceThemethod most commonlyused to describe the IQ An IQ is a positive numberthatintheory indicateshowa person smental altsofsuchtests is anintelligence quotient compareswiththeperson s chronological age ThemedianIQ is arbitrarily setat100sohalfthe populationhasan IQ lessthan andhalfgreater IQsaredistributed according to a bellcurvecalled a normalureThe proportion ofall peoplehavingIQs weenAand B isgivenbytheareaunderthecurvefrom AtoB stimatethe proportion all peoplehavingIQs ween120and126 44 1 1 e I FNdx I 2 2 14846 12 I21 1213 he is 126 f 1201 4 f 121 2f 1221 4f 123 27124 44125 f 126 0 4578 1 6904 0 7771 1 4235 0 6493 1 1801 0 2671 hp ana error approxvalue actualvalue obtain abound on the errorofusingthe trapezoidal rule with n 20 to approx S e dx I ex 6 A be in the theorem is always increasing its greatest value since 4 2 2 e onthe interval 10 1 occurs at 4 I 2 e be 278 0 0033980

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