Pre-Calc Homework Solutions 251

Pre-Calc Homework Solutions 251 - Section 6.3 3 Let u du ln...

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Unformatted text preview: Section 6.3 3. Let u du ln y 1 dy y 1 2 y ln y 2 1 2 y ln y 2 1 2 y ln y 2 1 2 y 2 251 dv v 1 dy y y dy 1 2 y 2 6. Let u du sin 1 1 dv 2 d 1 1 v 1 y ln y dy sin Let w dw sin d 1 2 sin 1 1 2 d 1 y dy 2 1 2 y C 4 2 d 1 1 1 2 1 2 d 1 2 Check: y ln y y C 4 dy 2 1 2 1 1 y (ln y)(y) y 2 y 2 d sin sin sin 1 1 1 1 2 1 w 1/2 dw C 2 w 1 C y ln y 4. Let u du tan Let w dw y tan 1 1 tan 1 1 y y2 dv dy 1 dy y y y2 1 v y 1 y dy 1 y tan y2 dy [ 1, 1] by [ 0.5, 2] 7. Let u du y y2 t2 2t dt dv v t 2 cos t dv v 2 t cos t dt 2t sin t 2t sin t sin t dt cos t 2 (cos t)(t) dt cos t dt sin t 2y dy y 1 dy y tan y tan y tan 1 1 1 y y y 1 2 1 2 1 2 1 dw w t 2 sin t dt C y 2) C Let u du t 2 cos t t dt ln w ln (1 Check: y 1 d y tan 1 y dy y2 tan 1 y dv v 1 ln (1 y 2) 2 1 1 (2y) 2 1 y2 C tan 1 y t 2 cos t t cos t (2 2 2 sin t dt 2 cos t C C 5. Let u du x dx sec2 x dx tan x tan x dx sin x dx cos x t 2) cos t 2t sin t x sec2 x dx x tan x x tan x x tan x ln cos x C [ 3, 3] by [0, 8] 8. Let u du t dt dv v t cot t t cot t t cot t csc2 t dt cot t cot t dt cos t dt sin t t csc2 t dt [ 1.5, 1.5] by [ 1, 4] ln sin t C [0, 3] by [ 4, 4] ...
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This note was uploaded on 10/05/2011 for the course MAC 1147 taught by Professor German during the Spring '08 term at University of Florida.

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