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# maths Math 1760

Toledo

GPA 3.96

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## Popular in Calculus 2 App

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This 2 page Class Notes was uploaded by Amalachi Notetaker on Thursday September 29, 2016. The Class Notes belongs to Math 1760 at University of Toledo taught by Susan Vayo in Fall 2016. Since its upload, it has received 5 views. For similar materials see Calculus 2 App in Natural Sciences and Mathematics at University of Toledo.

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Date Created: 09/29/16

p. 334: x − 1 1 1 1 4 24. ∫ 4 dx = ∫ du = ln |x – 4x| + C x − 4x 4 u 4 1 u = x – 4x du = (4x – 4) dx du = (x – 1) dx 4 32. ∫ sin xcosx dx= u d∫ = u + C = sin x + C 4 4 4 u = sin x du = cos x dx 1 2 2 0 1/2 4 2 1 4 1/2 2 3/2 58. ∫0 x √ − x dx = ∫4 u ( - ½ du) = -0 u (− d2) = ½ ∫0 u du = ½ ( 3u | x =0 to x= 4 2 3/2 3/2 8 u = 4 – x = 1/3(4) – 1/3(0) = 3 du = - 2xdx - ½ du = x dx u |x = 0 4 – 0 = 4 u |x = 2 4 – 2 = 0 p. 342: −x/2 -x/2 −x/2 -x/2 −x/2 8. ∫ 3xe dx = 3[-2xe -∫ −2e dx] = -6xe + 6∫???? dx -x/2 -x/2 -x/2 u = x dv = e dx = 6xe + 6(-2)e + C du = dx V = -2e -x/2 = 6xe -x/-12e -x/+ C ???? ???? 2 20. ∫ lnx = x ln x -2 ∫ x( ) dx = x ln x – 2x | x=1 to x = e ln e – 2e –[ ln 1 – 2(1)] 1 1 x u = ln x dv = dx = 2e – 2e – 0 + 2 = 2 du = 1 (2x) dx v = x x2 1 du = x dx ????/6 ????/6 26. ∫ ???? cos x dx = e cos x + ∫ ???? sin x dx 0 0 u = cos x dv = e dx du = -sin x dx v = ex ∫ ????/6???? cos x dx = e cos x + ∫ ????/6???? sin x dx = e cos x + e sin x - ∫????/6 ???? cos x dx 0 0 0 u = sin x dv = e dx du = cos x dx v = ex 2 ∫????/6 ???? cos x dx = e cos x + e sin x | x = 0 to x/6 0 ????/6 x x x ∫0 ???? cos x dx = ½ (e cos x + e sin x | x = 0 to /6= ???? ???? = ½ (????????/6 cos + ???? ????/6sin - (e cos 0 + e sin 0)) 6 6 ????/6 √3 ????/6 = ½ (???? ( 2 + ???? (1/2) – (1)(1) – (1)(0)) =(√ 3+ ) ???? ????/6 - 1 4 4

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