Lesson5.8InverseTrigFunctions-Integration

Lesson5.8InverseTrigFunctions-Integration - • Remember...

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Inverse Trigonometric Functions: Integration Lesson 5.8
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Review Recall derivatives of inverse trig functions 2 1 2 1 2 1 2 1 sin , 1 1 1 tan 1 1 sec , 1 1 d du u u dx dx u d du u dx u dx d du u u dx dx u u - - - = < - = + = < -
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Integrals Using Same Relationships 3 2 2 2 2 2 2 arcsin 1 arctan 1 arcsec du u C a a u du u C a u a a du u C a a u u a = + - = + + = + - When given integral problems, look for these patterns When given integral problems, look for these patterns
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Identifying Patterns For each of the integrals below, which inverse trig function is involved? 4 2 4 13 16 dx x + 2 25 4 dx x x - 2 9 dx x -
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Warning Many integrals look like the inverse trig forms Which of the following are of the inverse trig forms? 5 2 1 dx x + 2 1 x dx x + 2 1 dx x - 2 1 x dx x - If they are not, how are they integrated? If they are not, how are they integrated?
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Try These Look for the pattern or how the expression can be manipulated into one of the patterns 6 2 8 1 16 dx x + 2 1 25 x dx x - 2 4 4 15 dx x x - + + 2 5 10 16 x dx x x - - +
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Completing the Square Often a good strategy when quadratic functions are involved in the integration
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Unformatted text preview: • Remember … we seek (x – b) 2 + c Which might give us an integral resulting in the arctan function 2 2 10 dx x x + + Completing the Square • Try these 2 2 2 4 13 dx x x-+ + 2 2 4 dx x x-+ Rewriting as Sum of Two Quotients • The integral may not appear to fit basic integration formulas May be possible to split the integrand into two portions, each more easily handled 2 4 3 1 x dx x +-Basic Integration Rules • Note table of basic rules Page 364 • Most of these should be committed to memory • Note that to apply these, you must create the proper du to correspond to the u in the formula cos sin u du u C = + Assignment • Lesson 5.8 • Page 366 • Exercises 1 – 39 odd 63, 67 11...
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Lesson5.8InverseTrigFunctions-Integration - • Remember...

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