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# HW9 - x 1 ´ dx = R 1-1 sin x cos 2 x dx = R 1-sec 2 x-sin...

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Math 191 HW 9 Solutions 7.8: 8 cosh 3 x - sinh 3 x = e 3 x + e - 3 x 2 - e 3 x - e - 3 x 2 = e - 3 x 7.8: 10 ln(cosh x + sinh x ) + ln(cosh x - sinh x ) = ln(cosh 2 x - sinh 2 x ) = ln 1 = 0 7.8: 14 y = 1 2 sinh(2 x + 1) dy dx = 1 2 [cosh(2 x + 1)](2) = cosh(2 x + 1) 7.8: 26 y = cosh - 1 2 x + 1 = cosh - 1 (2( x + 1) 1 / 2 ) dy dx = (2)( 1 2 )( x +1) - 1 / 2 [2( x +1) 1 / 2 ] 2 - 1 = 1 x +1 4 x +3 = 1 4 x 2 +7 x +3 8.1: 4 R cot 3 y csc 2 ydy ; ± u = cot y du = - csc 2 ydy ² R u 3 ( - du ) = - u 4 4 + C = - cot 4 y 4 + C 8.1: 42 R dx ( x - 2) x 2 - 4 x +3 = R dx ( x - 2) ( x - 2) 2 - 2 ; ± u = x - 2 du = dx ² R du u u 2 - 1 = sec - 1 | u | + C = sec - 1 | x - 2 | + C, | u | = | x - 2 | > 1 8.1: 52 R 2 θ 3 - 7 θ 2 +7 θ 2 θ - 5 = R [( θ 2 - θ + 1) + 5 2 θ - 5 ] = θ 3 3 - θ 2 2 + θ + 5 2 ln | 2 θ - 5 | + C 8.1: 62 R 1 1 - csc x dx = R sin x sin x - 1 dx = R ³ 1 + 1 sin x - 1 ´ dx = R ³ 1 + sin x +1 (sin x - 1)(sin
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Unformatted text preview: x +1) ´ dx = R ( 1-1+sin x cos 2 x ) dx = R ( 1-sec 2 x-sin x cos 2 x ) dx = R (1-sec 2 x-sec x tan x ) dx = x-tan x-sec x + C 8.1: 66 R-π √ 1 + cos tdt = R-π √ 2 µ µ cos t 2 µ µ dt ; ± cos t 2 ≥ for-π ≤ t ≤ π ² → R-π √ 2 cos t 2 dt = [2 √ 2 sin t 2 ]-π = 2 √ 2[sin 0-sin(-π 2 )] = 2 √ 2 1...
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