Re: [理工] [工數]-fourier
看板Grad-ProbAsk作者CRAZYAWIND (考試快到了!!)時間16年前 (2010/03/01 21:28)推噓15(15推 0噓 40→)留言55則, 7人參與討論串7/8 (看更多)
※ 引述《uniqueco (寶)》之銘言:
: 請問
: 1 2 -inπx 2 2 -inπx
: ∫ (x + x)e dx + ∫ (x + x + 1)e dx
: 0 1
: 這種積分只能一直分部積分沒什麼技巧嗎?
: 類似這種的我每次整到後來都亂掉了...
: 謝謝
分開來算
x^2+x e^-inπx
i
-(2x+1) ──e^-inπx
nπ
1
2 -────e^-inπx
(nπ)^2
i
0 - ──── e^-inπx
(nπ)^3
2i 3 2i 1 2i
= ───(-1)^n + ────(-1)^n - ─── (-1)^n - ──── + ─────
nπ (nπ)^2 (nπ)^3 (nπ)^2 (nπ)^3
x^2+x+1 e^-inπx
i
-(2x+1) ──e^-inπx
nπ
1
2 -────e^-inπx
(nπ)^2
i
0 - ──── e^-inπx
(nπ)^3
7i 5 2i 3i 3 2i
= ──── + ──── -──── - ────(-1)^n -────(-1)^n +───(-1)^n
nπ (nπ)^2 (nπ)^3 nπ (nπ)^2 (nπ)^3
4 1 7i
兩個加起來 = ──── - ────(-1)^n + ────
(nπ)^2 nπ nπ
上面也有一篇跟這個類似的= = 不知道兩個誰的題目有錯
哭哭 我要抱怨一下台大生機這樣考會不會到最後不足額錄取阿= =
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◆ From: 59.105.159.190
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※ 編輯: CRAZYAWIND 來自: 59.105.159.190 (03/01 21:47)
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03/01 21:45, , 30F
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