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Class Note for MATH 1432 at UH 2


Class Note for MATH 1432 at UH 2

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This 15 page Class Notes was uploaded by an elite notetaker on Friday February 6, 2015. The Class Notes belongs to a course at University of Houston taught by a professor in Fall. Since its upload, it has received 17 views.

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Date Created: 02/06/15
Example 1 x17x2dacVcoszucosuducos2udu 1 1 1 1 7lt 50052ugt du7 uzsln2u0 usinucosu0 ltsin 1xam17ac2 0 Sine Substitution xa2 7 x2 Sine Substitution xa2 7 x2 1 7 sin2u cos2u ac asinu dac acosudu a2 7 x2 a2 COSZU Example 2 Vaz7x2dxVa2cos2uacosudua2 c0s2udu 1 1 7 2 7 7 7a lt2260s2ugt 2 2 2 du usin2u0 usinucosuC a2 2 sin 1x1iac2 0 Example Area of a Circle J A 7quot Sine Substitution a2 7 x2 2 1 7 sin u cos2 u ac asinu dx acosudu 2 2 2 2 a 7x a cos u Example 3 39r2iac2dx 7 ma cos2 u du g Vr2cos2u39rc0sudu39r g 1 1 g 7 2 7 7 I 77 2u4sin2u7 ma W72 7 area enclosed by a semicircle of radius 39r gtltY Example Completing the Square Sine Substitution H12 7 ac 7 c2 17sin2u cos2u x7 c asinu dac acosudu a2 7 ac 7c2 112005211 Example 4 27x24xdx 247ac24x4dx x67ac722dx6cos2udu usinucosu0 3ltsin 1L 2 6 67x722gt 0 ac727isinu7 dac cosudu7 67x72260052u Sine Substitution Va2 7 x2 Sine Substitution Va2 7 x2 1 7 sin2u coszu ac asinu dac acosudu a2 7 x2 a2 00521 Example 5 4 7 2 m 0052 u 751 172005111111 du 55 2 slnu 5111 7 2 g du2cscu7sinudu smu 2h1cscu7cotu2wsu0 J 7 2 gm g 42Cm 12 Tangent Substitution Tangent Substitution 1 x2 Tangent Substitution 1 2 1tan2u seczu x tanu dx seczudu 1 2 seczu Example 6 1 1 2 2 demsec uducos udu 1 1 1 1 7lt 0052ugt du ulsin2u0 2 usinucosu0 llttan 1xLgtCH 2 W W Tangent Substitution xa2 x2 Tangent Substitution Va2 x2 1 tan2u sec2u ac atanu dac asec2udu a2 x2 a2 sec2u Example 7 Va2x2dapVa2sec2uasec2uduaZsecgudu 2 secutanuln secu tanu 0 gto Example 3 Tangent Substitution 112 352 1tan2usec2u xatanu dxasec2udu a2 x2 a2 sec2u Example 8 1 1 1 3 idxi isec2udu z94x2 2 gum 5802 2 1 secu 1 igmduigcscudu 1 gln cscuicotuPrC 1 V9 4 273 7ln x 0 3 235 Example Tangent Substitution Va2 x2 1 tan2u sec2u ac atanu dac aseCZudu a2 x2 a2 sec2u Example 9 V 4t 2 8t 2 2 3 zseCZudumdu 2 ac in 42 V44tan2u 4sec2u 8t 2 2 mdu4tan2usecudu ZSecu nish as in Example 12 Section 83 substitute in terms of ac Example Completing the Square Tangent Substitution a2 ac 7 c2 1tan2usec2u x70 atanu dac aseCZudu 12 ac 7 c2 a2 sec2u Example 10 am16x276xdacxw1679x276x9dx xx7ac732dx tanu3 V7sec2u sec2udu Finishit 13 Secant Substitution Secant Substitution x2 7 1 10 sec 1x Secant Substitution 22 7 1 seczu7 1 tanzu 2 secu dzz secutanudu 22 7 1tan2u Example 11 1 d see u tan u d 1 d a u u 122 22 7 1 sec2 uv tan2 u see u cosudusinuC 271 LJVC 2 Secant Substitution 22 7 a2 11 Secant Substitution v12 7 a2 seczu 71tan2 u z asecu dz asecutanudu 12 7 a2 a2 tanzu Example 12 1 d 2 sec utan u 1 1 I u 7 112 7 4032 2562u4tan2 u32 8 0502 u 7 1 du tan2 u 1 1 gCotzudu7 1 7cotu7uC 1 g sec 1z2gt 0 Example Completing the Square 12 x lx2 4 u 2 Secant Substitution v12 7 a2 sec2 u71tan2u If c asecu dz asecutanudu If c2 7122 a2 tanzu Example 13 dzdz VIZ2173 xIZ21173161 7dz 1 12 74 2562014712 t d 7 secu anu u V4tan2u Finish it S ailwary 17 sin2 u coszu z asinu dz acosudu 12 i 12 ZZCOSZU 13 Ll a2 x2 ac s1nu7 a 12152 cosu a an tanu 12152 a2x2 1tan2usec2u atanu dacasec2udu a22a2sec2u 35L 7 X G Ll sinu Va 362 a cosu 4 a2 12 x tanu 7 a x fag sec2 u i 1 tam2 u x asecu 120 i asecutanudu x2 i a2 i a2 tam2 u X sz 4 Ll 2 7 a2 sinu x cosu 7 2 7 a2 tanu a Outline Contents 1 Trigonometric Substitution 11 Sine Substitution 12 Tangent Substitution 13 Secant Substitution 15 1 OOTHH Lecture 9Section 84 Integrals Involving Va2 722 Va2 22 V752 7a2 Trigonometric Substitutions J iwen He 1 Trigonometric Substitution 11 Sine Substitution Sine Substitution V1 7 22 sin1x Sine Substitution V1 7 22 17sin2u c052u zsinu dz cosudu 1 7 22 c052u


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