Sec 7.5 : STRATEGY FOR INTEGRATION

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Presentation transcript:

3 1 2 3 4 6 7 5 8 9 Sec 7.5 : STRATEGY FOR INTEGRATION Classify the integrand according to Its form 1 2 Integrand contains: Integrand contains: ln and its derivative f and its derivative by parts by parts We know how to integrate all the way 3 4 Integrand = Integrand radicals: by parts (many times) 7.3 PartFrac 6 Integrand = rational Radicals with different indexes f & f’ 7 Back to original 2-times by part  original 5 Integrand contains: only trig 7.2 8 9 Rational sine & cosine: Combination:

Sec 7.5 : STRATEGY FOR INTEGRATION 132 131 Partial fraction Simplify integrand Radicals(Trig subs) f & f’ conjugate radical with diff index Trig fns by parts Power of Others(identity) Obvious subs Rational in sin & cos several original Back

Sec 7.5 : STRATEGY FOR INTEGRATION 132 131 Partial fraction Simplify integrand Radicals(Trig subs) f & f’ conjugate radical with diff index Trig fns by parts Power of Others(identity) Obvious subs Rational in sin & cos several original Back

OLD EXAMS: TERM 121 121

Sec 7.5 : STRATEGY FOR INTEGRATION Partial fraction Simplify integrand Radicals(Trig subs) f & f’ conjugate radical with diff index Trig fns by parts Power of Others(identity) Obvious subs Rational in sin & cos several original Back

Sec 7.5 : STRATEGY FOR INTEGRATION Partial fraction Simplify integrand Radicals(Trig subs) f & f’ conjugate radical with diff index Trig fns by parts Power of Others(identity) Obvious subs Rational in sin & cos several original Back

OLD EXAMS: TERM 133 133

OLD EXAMS: TERM 101 101

OLD EXAMS: TERM 101 101

OLD EXAMS: TERM 101 101

OLD EXAMS: TERM 101 101

OLD EXAMS: TERM 101 101

OLD EXAMS: TERM 101 101

Sec 7.5 : STRATEGY FOR INTEGRATION Partial fraction Simplify integrand others Radicals(Trig subs) f & f’ conjugate radical with diff index Trig fns by parts Power of Others(identity) Obvious subs Rational in sin & cos several original Back

Sec 7.5 : STRATEGY FOR INTEGRATION Partial fraction Simplify integrand others Radicals(Trig subs) f & f’ conjugate radical with diff index Trig fns by parts Power of Others(identity) Obvious subs Rational in sin & cos several original Back