推 cuttlefish : arccos裡的z忘了加√ 12/26 13:35
謝謝，已更正
※ 編輯: Honor1984 (61.56.10.112), 12/26/2016 13:43:45
※ 引述《CyCls (CyCls)》之銘言：
: http://i.imgur.com/l0esjSv.jpg 請問Z要怎麼求呢？謝謝
dz/dx = (1/c)√[(1/z) - c^2]
=> {1/√[(1/z) - c^2]} dz = dx/c
LHS = √z / √[1 - zc^2]dz
令[cosθ]^2 = zc^2
LHS = √[(cosθ)^2] / √[(sinθ)^2] * (1/|c|) * (1/c^2) 2(cosθ)(-sinθ)dθ
= 2(cosθ)^2 dθ / [|c|c^2]
= [θ + (1/2)sin(2θ)]/(|c|^3)
= {arccos(|c|√z) + |c|√z * √[1 - zc^2]} / |c|^3
=> {arccos(|c|√z) + |c|√z * √[1 - zc^2]} / |c|^3 = x/c + Const
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