作者pboywc (AC)
看板trans_math
标题Re: [积分] 请帮个忙
时间Wed Apr 12 01:29:11 2006
※ 引述《boxgene (原来什麽事情都不简单)》之铭言：
: Prove the following statement :Let f be a positive continuous function
: on [0 ，1] . Suppose that
: 1 1
: S f(x) dx=a and S f(x^2) dx =b
: 0 0
: Then a<２b
: ¯
: 请问这要怎麽做
1 1
令x=t^2 a=S 2tf(t^2)dt =2S xf(x^2)dx
0 0
1 1
2b-a=2S f(x^2)dx - 2S xf(x^2)dx
0 0
1
2S (1-x)f(x^2)dx > 0
0
a<2b
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※ 发信站: 批踢踢实业坊(ptt.cc)
◆ From: 218.34.243.63
1F：推 boxgene:S(1-x)f(x^2)dx <=怎麽知道他大於零....谢谢 04/12 20:40
2F：推 pboywc:x在0和1之间 f(x)恒正由题设 04/12 23:28
3F：推 boxgene:(1-x)不会有影响吗 04/13 00:54