Re: [微積] 瑕積分
看板trans_math作者PaulErdos (My brain is open)時間13年前 (2010/12/25 21:45)推噓3(3推 0噓 4→)留言7則, 3人參與討論串3/4 (看更多)
※ 引述《dreamingaway (Wherever I May Roam)》之銘言:
: ※ [本文轉錄自 Math 看板 #1D5M3XID ]
: 作者: dreamingaway (Wherever I May Roam) 看板: Math
: 標題: [微積] 瑕積分
: 時間: Sat Dec 25 11:11:26 2010
: Discuss the convergence or divergence of the integrals
: ∞ ∞
: ∫(sinx/x)dx and ∫(|sinx|/x)dx
: 0 0
: 謝謝
kπ sinx
Denote A = ∫ ── dx
k (k-1)π x
∞ sinx
then ∫ ── dx = ΣA is an alternating series .
0 x k
kπ │sinx│ 1 kπ
Since │A │ ≧ ∫ ──── dx = ─ ∫ │sinx│ dx
k (k-1)π kπ kπ (k-1)π
1
= ─ ‧ 2
kπ
2 1
so Σ│A │ ≧ ─ Σ─
k π k
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