※ 引述《feathersss (不定)》之铭言： : 请问几题： : 1.Find the surface area of the surface of revolution generated by revolving : the arc of unit circle x^2+y^2=1 in the first quadrant about the ling x+y=1. : 只会做绕x轴或y轴的~这种绕直线的要怎麽做呢? : 2.Show that：if f'(c)<0, then f has no extreme value at c. : 3.Show that the improper integral 1/√2π∫e^(-t^2/2) dt 从-∞积到x : converges for all real number x. 1. |x+y-1| 点 (x,y) 到 直线 x+y=1 的距离 d(x,y) = --------- 2^1/2 所求为 2πd(x,y) 在 C: x^2+y^2=1 in the first quadrant 上的线积分 即 ∫ 2πd(x,y) ds C C: x=cosθ , y=sinθ , 0≦θ≦π/2 ds = (x'(θ)^2 + y'(θ)^2) dθ = dθ π/2 |cosθ+sinθ-1| 所求 = ∫ 2π ---------------- dθ = ....... 0 √2 --

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