作者Honor1984 (希望愿望成真)
看板trans_math
标题Re: [积分] 黎曼和
时间Thu Aug 20 00:17:11 2009
※ 引述《midarmyman (midarmyman)》之铭言：
: 函数sinx从0积到pi
: 用梯形法写
: pi/2n﹝f(0)+2f(pi/n)+2f(2pi/n)+....+f(pi)﹞
: 然後取n趋近无限大 怎麽样才能算出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]
接下来取极限
2 1
=> -------------- = 2
1
如果每个简单积分都用离曼和求
恐怕会累死
更别说是复杂函数
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◆ From: 122.124.103.225
※ 编辑: Honor1984 来自: 122.124.103.225 (08/20 00:20)
1F：推 midarmyman:第一行把二除进去 最後一项应该是 114.38.156.190 08/20 22:17
2F：→ midarmyman:f(pi)/2吧? 114.38.156.190 08/20 22:17
3F：→ Honor1984:有差吗? f(π)=? 其实有没有都无所谓122.124.108.252 08/20 22:22
4F：推 midarmyman:水球丢我ㄧ下 我还有其他问题 114.38.156.190 08/20 22:28
5F：→ midarmyman:有些地方不太懂 谢谢 114.38.156.190 08/20 22:28
6F：推 midarmyman:为啥偶数项都不见了? 还有为啥会用两 114.38.156.190 08/20 22:35
7F：→ midarmyman:倍角? 114.38.156.190 08/20 22:35
8F：推 midarmyman:站内信 114.38.156.190 08/20 23:19