Basic Integration RulesFitting Integrals to Basic RulesTry It OutThe Log Rule in DisguiseThe Power Rule in DisguiseSlide 6Disguises with Trig IdentitiesAssignmentBasic IntegrationRulesLesson 8.1Fitting Integrals to Basic Rules•Consider these similar integrals•Which one uses …The log ruleThe arctangent ruleThe rewrite with long division principle22 2 25 5 54 4 4x xdx dx dxx x x+ + +� � �Try It Out•Decide which principle to apply …21xdxx +�( )222 1 4dtt - +�The Log Rule in Disguise•Consider•The quotient suggests possible Log Rule, but the du = ex is not present•We can manipulate this to make the Log Rule apply Add and subtract ex in the numerator11xdxe+�11x xxe edxe+ -+�1...1 1x xx xe edx dxe e+= -+ +� �The Power Rule in Disguise•Here's another integral that doesn't seem to fit the basic options•What are the options for u ?•Best choice is( ) ( )cot ln sinx x dx�� �� ��( )cosln sin cotsinxu x du dx x dxx= = =The Power Rule in Disguise•Thenbecomes and power rule applies •Note review of basic integration rules pg 520•Note procedures for fitting integrands to basic rules, pg 521( ) ( )cot ln si nx x dx�� �� ��u du�Disguises with Trig Identities•What rules might this fit?•Note that tan2 u is not on the list …However sec2u is on the list•This suggests one of the pythagorean identities and we have2tan 2x dx�21sec 12u du-�Assignment•Lesson 8.1•Page 522•Exercises 1 – 49
View Full Document
Unlocking...