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Pre-Calc Homework Solutions 471

# Pre-Calc Homework Solutions 471 - Appendix A6/4 1 ln 10 1...

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55. E p /4 2 p /4 cosh (tan u ) sec 2 u d u 5 E 1 2 1 cosh u du 5 3 sinh u 4 5 sinh (1) 2 sinh ( 2 1) 5 1 } e 1 2 2 e 2 1 } 2 2 1 } e 2 1 2 2 e 1 } 2 5 5 e 2 e 2 1 < 2.350, where u 5 tan u , du 5 sec 2 u d u , the lower limit is tan 1 2 } p 4 } 2 5 2 1 and the upper limit is tan 1 } p 4 } 2 5 1. 56. E p /2 0 2 sinh (sin u ) cos u d u 5 2 E 1 0 sinh u du 5 2 3 cosh u 4 5 2(cosh 1 2 cosh 0) 5 2 1 } e 1 2 e 2 1 } 2 1 2 5 e 1 e 2 1 2 2 < 1.086, where u 5 sin u , du 5 cos u d u , the lower limit is sin 0 5 0 and the upper limit is sin 1 } p 2 } 2 5 1 57. E 2 1 } cosh t (ln t ) } dt 5 E ln 2 0 cosh u du 5 3 sinh u 4 5 sinh (ln 2) 2 sinh (0) 5 } e ln 2 2 2 e 2 ln 2 } 2 0 5 5 } 3 4 } , where u 5 ln t , du 5 } 1 t } dt , the lower limit is ln 1 5 0 and the upper limit is ln 2 58. E 4 1 } 8 co ˇ sh x w ˇ x w } dx 5 16 E 2 1 cosh u du 5 16 3 sinh u 4 5 16(sinh 2 2 sinh 1) 5 16 31 } e 2 2 2 e 2 2 } 2 2 1 } e 2 2 e 2 1 } 24 5 8( e 2 2 e 2 2 2 e 1 e 2 1 ) < 39.227, where u 5 ˇ x w 5 x 1/2 , du 5 } 1 2 } x 2 1/2 dx 5 } 2 d ˇ x x w } , the lower limit is ˇ 1 w 5 1 and the upper limit is ˇ 4 w 5 2.
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