Pre-Calc Homework Solutions 363

Pre-Calc Homework Solutions 363 - Chapter 8 Review 68 For x...

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Unformatted text preview: Chapter 8 Review 68. For x 66. x 1 (1 363 0, y xe 0 0 on [0, ). x x b sin , dx x2 cos2 cos d , 2 2 Area dx lim b 0 xe x dx Evaluate xe 4 sin2 3 dx by using integration by parts. dv e e e x x x 4x 2 dx x 2)3/2 cos d u du xe x dx x dx cos 4(1 cos2 ) d cos2 v xe xe x x dx lim b dx b 0 xe x e x C (4 sec 4 tan 4x 1 2 4) d Area 4 C 4 sin 1. dx dt dx (a 1 e e x lim [ be b b b 1] x2 x C Use Figure 8.18(b) with a 67. For x Volume 0 1 0 1 b b eb 1 lim b b e lim 1 1 1 b 0, y 1 0 on (0, 1]. ( ln x)2 dx (ln x) dx lim b0 2 69. (a) k(a x)2 k dt k dt kt C 0, t 0 kt C1 C1 (ln x)2 dx Evaluate u du (ln x) 2 (ln x)2 dx by using integration by parts. dv v x (ln x) 2 dx x 2 ln x dx x)2 dx (a x)2 1 C2 a x 1 kt a x 1 a 1 a x 1 kt 1/a Substitute x C kt a 1 kt 2 ln x dx x 2 (ln x) dx Evaluate 2 ln x dx by using integration by parts. u du 2 ln x 2 dx x 1 a x 1/a dv v 2x ln x x (ln x)2 x(ln x)2 x dx x a 2 ln x dx (ln x)2 dx Area 2 dx 2x ln x 2x ln x 2x 2x b 2x C 1 C lim b0 2x ln x lim [2 b0 b(ln b)2 (ln b)2 1/b 2b ln b 2 lim b0 2b] 2 2 2 2 lim b0 ln b 1/b b0 lim b0 2 (ln b)(1/b) 1/b2 2 (ln b) 1/b 2 /b 1/b2 2 lim /b 1/b2 lim b0 2 lim ( b0 b) 2 lim b0 2 lim 2 b b0 ...
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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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