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Pre-Calc Homework Solutions 249

# Pre-Calc Homework Solutions 249 - Section 6.3 50(a u cot 2...

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50. (a) u 5 cot 2 u , du 5 2 2 csc 2 2 u d u E csc 2 2 u cot 2 u d u 5 2 } 1 2 } E u du 5 2 } 1 2 } ? } u 2 2 } 1 C 5 2 } u 4 2 } 1 C 5 2 } 1 4 } cot 2 2 u 1 C F 1 ( u ) 5 2 } 1 4 } cot 2 2 u (b) u 5 csc 2 u , du 5 2 2 csc 2 u cot 2 u d u E csc 2 2 u cot 2 u du 5 2 } 1 2 } E u du 5 2 } 1 2 } ? } u 2 2 } 1 C 5 2 } u 4 2 } 1 C 5 2 } 1 4 } csc 2 2 u 1 C F 2 ( u ) 5 2 } 1 4 } csc 2 2 u (c) F 1 9 ( u ) 5 1 2 } 1 2 } cot 2 u 2 ( 2 2 csc 2 2 u ) 5 csc 2 2 u cot 2 u F 2 9 ( u ) 5 1 2 } 1 2 } csc 2 u 2 ( 2 2 csc 2 u cot 2 u ) 5 csc 2 2 u cot 2 u (d) F 1 ( u ) 5 F 2 ( u ) 1 b 2 } 1 4 } cot 2 2 u 5 2 } 1 4 } csc 2 2 u 1 b b 5 } 1 4 } (csc 2 2 u 2 cot 2 2 u ) 5 } 1 4 } 1 2 5 } 1 4 } 1 } s s i i n n 2 2 2 2 u u } 2 5 } 1 4 } 51. (a) u 5 sin x , du 5 cos x dx E 2 sin x cos x dx 5 E 2 u du 5 u 2 1 C 5 sin 2 x 1 C (b) u 5 cos x , du 5 2 sin x dx E 2 sin x cos x dx 5 E ( 2 2 u ) du 5 2 u 2 1 C 5 2 cos 2 x 1 C (c) u 5 2 x , du 5 2 dx E 2 sin x cos x dx 5 E sin 2 x dx 5 E } 1 2 } sin u du 5 2 } 1 2 } cos u 1 C 5 2 } 1 2 } cos 2 x 1 C (d) } d d x } (sin 2 x 1 C ) 5 2 sin x cos x } d d x } ( 2 cos 2 x 1 C ) 5 ( 2 2 cos x )( 2 sin x ) 5 2 sin x cos x } d d x } 1 2 } 1 2 } cos 2 x 1 C 2 5 1 } 1 2 } sin 2 x 2 (2) 5 sin 2 x 5 2 sin x cos x Section 6.3 Integration by Parts (pp. 323–329) Exploration 1 Evaluating and Checking
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