作者Honor1984 (希望願望成真)
看板trans_math
標題Re: [積分] 黎曼和
時間Thu Aug 20 00:17:11 2009
※ 引述《midarmyman (midarmyman)》之銘言：
: 函數sinx從0積到pi
: 用梯形法寫
: pi/2n﹝f(0)+2f(pi/n)+2f(2pi/n)+....+f(pi)﹞
: 然後取n趨近無限大 怎麼樣才能算出2呢?
= π/n [f(π/n)+f(2π/n)+....f(π)]
= π/(-2)nsin(π/2n) {-cos[π/2n]+cos[3π/2n] ...... +cos[(2n+1)π/2n]}
= π/(-2)nsin(π/2n) {cos[(2n+1)π/2n]-cos[π/2n]}
= π/(-2)nsin(π/2n) * (-2)sin[(n+1)π/2n]sin[nπ/2n]
πsin[(n+1)π/2n]
= -----------------
n sin[π/2n]
π cos[π/2n]
= --------------
n sin[π/2n]
接下來取極限
2 1
=> -------------- = 2
1
如果每個簡單積分都用離曼和求
恐怕會累死
更別說是複雜函數
--
※ 發信站: 批踢踢實業坊(ptt.cc)
◆ From: 122.124.103.225
※ 編輯: Honor1984 來自: 122.124.103.225 (08/20 00:20)
推 midarmyman:第一行把二除進去 最後一項應該是 114.38.156.190 08/20 22:17
→ midarmyman:f(pi)/2吧? 114.38.156.190 08/20 22:17
→ Honor1984:有差嗎? f(π)=? 其實有沒有都無所謂122.124.108.252 08/20 22:22
推 midarmyman:水球丟我ㄧ下 我還有其他問題 114.38.156.190 08/20 22:28
→ midarmyman:有些地方不太懂 謝謝 114.38.156.190 08/20 22:28
推 midarmyman:為啥偶數項都不見了? 還有為啥會用兩 114.38.156.190 08/20 22:35
→ midarmyman:倍角? 114.38.156.190 08/20 22:35
推 midarmyman:站內信 114.38.156.190 08/20 23:19