Re: [積分] 積分e積出拍

[suhorng ( )]

※ 引述《andy05227900 (小黑)》之銘言：
: 請問為什麼
: 積分區間0到正無限大e^-u^2du=根號拍/2
: 為什麼積分e可以積出拍??

Apostol 書中一個很神的做法

7.19 Define

            x                          1 e^{-x^2(t^2+1)}
  f(x) = ( ∫e^{-t^2} dt )^2,  g(x) = ∫-----------------dt
            0                          0     t^2 + 1
                                                                          π
  a) Show that g'(x) + f'(x) = 0 for all x and deduce that g(x) + f(x) = ---
                                             __                           4
                            ∞             √π
  b) Use (a) to prove that ∫e^{-t^2} dt = ----
                            0                2

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