Pre-Calc Homework Solutions 249

Pre-Calc Homework Solutions 249 - Section 6.3 50. (a) u cot...

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Unformatted text preview: Section 6.3 50. (a) u cot 2 , du 2 csc2 2 d 1 u du 2 1 u2 C 2 2 u2 C 4 1 cot2 2 C 4 249 (c) u 2x, du 2 dx sin 2x dx 1 sin u du 2 1 cos u C 2 1 cos 2x C 2 csc2 2 cot 2 d 2 sin x cos x dx F1( ) (b) u 1 cot2 2 4 (d) 2 csc 2 cot 2 d 1 u du 2 1 u2 C 2 2 u2 C 4 1 csc2 2 C 4 csc 2 , du csc2 2 cot 2 du d (sin2 x C) 2 sin x cos x dx d ( cos2 x C) ( 2 cos x)( sin x) dx 1 1 d cos 2x C sin 2x (2) 2 dx 2 2 sin x cos x sin 2x 2 sin x cos x s Section 6.3 Integration by Parts (pp. 323329) Exploration 1 Integrals 1. u ln x du ln x dx u dv uv v du dx x ln x dy dx F2( ) (c) F1 ( ) F2 ( ) 1 csc2 2 4 1 cot 2 ( 2 csc2 2 ) csc2 2 cot 2 2 1 csc 2 ( 2 csc 2 cot 2 ) 2 Evaluating and Checking dx and dv x dx v x. Thus, csc 2 cot 2 (d) F1( ) F2( ) b 1 csc2 2 4 2 1 cot2 2 4 b x ln x x ln x 1 4 b 1 (csc2 2 cot2 2 ) 4 1 1 cos2 2 1 sin2 2 sin2 2 4 4 sin2 2 C x 1 x 2. d (x ln x dx x) 1 ln x 51. (a) u sin x, du cos x dx 2u du sin x dx ( 2u) du u2 C C u 2 3. The slope field of C sin x 2 ln x shows the direction of the 2 sin x cos x dx (b) u cos x, du 2 sin x cos x dx C curve as it is graphed from left to right across the window. cos2 x [0, 6] by [ 2, 5] ...
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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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