作者Dirichlet ( )
看板Math
标题Re: [分析] 高微(6)
时间Thu Aug 11 20:10:10 2005
※ 引述《PttFund (批踢踢基金只进不出)》之铭言：
: Suppose that f has the derivative which is monotonic decreasing with
: f'(x) ≧ m > 0 on [a,b]. Show that
: b
: ∣∫ cos(f(x)) dx ∣ ≦2/m.
: a
b b
|∫ cos(f(x)) dx| = |∫ [cos(f(x))/f'(x)] df(x)|
a a
b
≦ (1/m) |∫ cos(f(x)) df(x)| = (1/m) |sin(f(b)) - sin(f(a))|
a
≦ 2/m
递减的条件好像没用到 ?
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※ 发信站: 批踢踢实业坊(ptt.cc)
◆ From: 61.219.178.230
1F：推 Sfly:有吧 在第一个不等号...220.135.132.108 08/11
2F：推 Dirichlet:你是指 R-S 积分啊 @@? 61.219.178.230 08/11