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## maths

by: Amalachi Notetaker

5

0

2

# maths Math 1760

Amalachi Notetaker
Toledo
GPA 3.96

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COURSE
Calculus 2 App
PROF.
Susan Vayo
TYPE
Class Notes
PAGES
2
WORDS
KARMA
25 ?

## Popular in Natural Sciences and Mathematics

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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### What is Karma?

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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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