Lesson5.8InverseTrigFunctions-Integration

Lesson5.8InverseTrigFunctions-Integration - Remember we...

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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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This note was uploaded on 01/18/2012 for the course MATHEMATIC 170 taught by Professor Dougbullock during the Spring '11 term at Boise State.

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Lesson5.8InverseTrigFunctions-Integration - Remember we...

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