Re: [積分] exponential的積分?
: 1.
: ∞
: ∫ e^-x^2 dx √π
: 0 Ans: --------
: 2
1.
令t=x^2
∞ ∞
∫ e^-x^2 dx = (1/2) *∫ (e^(-t))(t^(-1/2)) dt
0 0
= Γ(1/2)/2 = √π/2
: 2.
: ∞ 1 √π
: ∫ e^-(s+1)x^2 dx Ans: --- x --------
: 0 2 ↑ √(s+1)
: (這是乘號)
2.令t= (√(s+1)x)^2
∞ ∞
∫ e^-(s+1)x^2 dx = (1/2√(s+1)) * ∫ (e^(-t))* (t^(-1/2))dt
0 0
= (Γ(1/2)/2√(s+1)) = √π/[2√(s+1)]
我的方法還可以吧?OnlyGood
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