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Sec 7.5 : STRATEGY FOR INTEGRATION

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Presentation on theme: "Sec 7.5 : STRATEGY FOR INTEGRATION"— Presentation transcript:

1 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:

2 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

3 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

4 OLD EXAMS: TERM 121 121

5 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

6 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

7 OLD EXAMS: TERM 133 133

8 OLD EXAMS: TERM 101 101

9 OLD EXAMS: TERM 101 101

10 OLD EXAMS: TERM 101 101

11 OLD EXAMS: TERM 101 101

12 OLD EXAMS: TERM 101 101

13 OLD EXAMS: TERM 101 101

14 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

15 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

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