Pre-Calc Homework Solutions 347

Pre-Calc Homework Solutions 347 - Section 8.4 11. t 3 t3...

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Unformatted text preview: Section 8.4 11. t 3 t3 347 t2 1 t2 2t 2t t(t 2 A t t t B 2 2) t t(t C 1 2)(t 1) 15. x 2 x 1 5x 2 5x 2 1 A(t A(t 2 (A 2)(t t B 1) 2) C)t 2 B(t)(t B(t 2 (A t) B 1) C(t)(t 2t) 2A 2) x 2 5x 5x 5x 5 5 5 5 C(t 2 2C)t 5x 2 x 2 1 5 5x 5 x2 x 1 5x 2 dx x x 1 5 dx 5x 5 5 x2 x x2 x x 1 x 1 1 dx Equating coefficients of like terms gives A B C 0, A B 2C 0, and 2A 1. 1 dx Solving the system simultaneously yields A t 3 1 1 1 ,B ,C . 2 6 3 1/2 dt dt t t 2 2t 1 ln t 2 To evaluate the second integral, complete the square in the denominator. 1/3 dt t 1 1 ln t 1 3 1/6 dt t 2 1 ln t 6 x2 C x x2 x 1 x (x (x 1 1 x2 dx x 1 4 3 4 x 1 2 2 3 4 2 2) 12. 2t 3 8t 2t(t 2 A t t 4) B 2 2t(t C t 2 2)(t x 1 dx 1/2)2 3/4 x 1/2 dx 1/2)2 3/4 1 2 2 3 4 (x 1 2 (x 1 2 1 3 2 3 1/2 1/2)2 3/4 dx x 1 3 t 3 2t 3 8t dx t 3 2A(t 2A(t 2 (2A 2)(t 4) 2B 2) 2B(t 2 2C)t 2 2B(t)(t 2t) (4B 2) 2C(t 2 4C)t 2C(t)(t 2t) 8A 2) 1 ln x 2 1 ln (x 2 2 1 ln (x 2 2 1/2)2 ( 3/2)2 1/2 3/2 x x 1) 1) tan 1 1 Equating coefficients of like terms gives 2A 2B 2C 0, 4B 4C 1, 8A 3 tan 2x Solving the system simultaneously yields A t 2t 3 3 ,B 8 3 dt 8t 5 1 ,C . 16 16 3/8 5/16 dt dt t t 2 3 5 ln t ln t 2 8 16 The second integral was evaluated by using Formula 16 from the Brief Table of Integrals. x2 5x 2 dx x 1 5 ln (x 2 2 1/16 dt t 2 1 ln t 16 5x 2 C 16. (x x 1) 5 3 tan 1 2x 3 1 C 13. s 2 4 s 3s 3 s3 s 4s 4s 4s 4s s2 4 1)(x 2 x2 2 2x 1) (x A 1)(x B 1 x 1 1)2 C (x 1)2 (x 1)(x 2x 1) x s3 s2 s2 4 s3 4 x2 s ds 4s s2 4 2 A(x A(x 2 1)2 2x B)x 2 B(x 1) (2A 1)(x B(x 2 1) 1) A C(x C(x B C 1) 1) s ds 1 2 s 2 ds 4) C (A C)x 2 ln (s Equating coefficients of like terms gives A B 1, 2A C 0, and A B C 0. 14. s 2 s2 1 4 3 2 1 s + 0s + 0s 2s + 0 s 4 + s3 s 2+ s + 0 s 2 2s + 0 s2 + s 1 2s 1 1 (s 2 1 3 s 3 2s s2 1 1 Solving the system simultaneously yields A 1 ,B 4 (x 1 x 3 ,C 4 1) x 3/4 dx 1 (x 1/2 dx 1)2 1 2(x 1) 1 . 2 s 4 2s s2 s2 1 s 4 2s ds s2 1 s 2 1 2s ds s2 1 2s s2 s 1 ds 2 1 s2 1 x 2 dx 1)(x 2 2x 1/4 dx 1 1) ds s ln (s 2 1) tan 1 s C 1 ln x 4 1 3 ln x 4 1 C ...
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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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