6.1 Integration by Parts

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California State University, Long Beach *

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Mechanical Engineering

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Oct 30, 2023

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Note Show Your work 6.1 3,20 Due Wednesday Integration by Parts d luv adv t vdu adv d au v du fudu nu f vdu Examples 1 Xe dx dying a ex du e'd Xe fetdx Xe e t c 2 J R cos x dx u p du 2xdx TI g's Ig l f's sins d f x sin 3x 3 f x sin 2x dx u A du da du sin 3 x dy v t ios 3x Ix sin 3 x 3 B x cos Bx S 3105 Bx dx IN sin 3x t X 105 Bx f cos 3 x dx IN sin Zx x co x 227 Sin x C
Tabular Method 3x 2x I sin Bx 27 Sin x x cos x dx 3 2 sin x EX cos 3x 227 Sin x C Example 3 x e dx 15 fax É 5 4 e a 1 5 e 2x G x é x3é x'e 2x xe 2x 20 3 I e 2x IF e C 60 2 to e 2x 120 X t it e 2x 120 32 e 2x O tu e n 4 f An x dx int You stop when you x get a simple integration x lax f I x dx x tnx fax X In x Xt C
S f linx chap T x tnx f 2ft x dx Zen X X x tnx 2 In x dx x x tnx 2 x tnx ft x dx a du tnx T x tnx 2xtnx 2x C x I f sin x dx can't let a six t T be equal to 1 2 X x sin x Ife dx ft o f É 4 1 x2 o substitution du 2x dx x dx It iz f day Iz t 254 E I It E I 7 e cos 2x dx costa tf I e ios 2x E e sin 2x ta f e cos 2x dx brought to left hand 2 sin 2x te side of og euation 4 ios 2x ate e ios 2x dx t t e ios 2x dx te cos 2x Ee sin 2x Ia f e lol 2x dx Be cos 2x t e sin 2x f 3 d 3 2 3 x
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Se ios 2x dx e cos 2x t E es sin 2x t c 81 It e t dt n t Z du 2t dt f Fet tdt dy tdt Ju é de If u e d I ten I ne é C 1 é Effet it C o e é It e t I e t c 9 f e sin 70 do Tino 60 É e sin 70 367 cos 70 Jebb sin 70 do 710170 I e 60 49 sin 70 I e 60 it 436 f e 60 do I ebt sin 70 e cos 70 9361 S e sin 70 do te sin 70 I e 60 cos 70 C 10 19151 dx JE ax ax E if du É É ew we it a ew I we dw hwy YI f Ite w
YI tent C f we in e it w C E c f EI e It 2x C

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