作者damo (看见新的太阳)
看板trans_math
标题Re: [积分]这个要怎麽积/\
时间Wed Aug 16 15:38:31 2006
※ 引述《black0920 (PH值小於7  )》之铭言：
: 4
: 求∫ x d[x]=?
: 2
Lemma:if f is belong to C(R) and s is belong to (a,b] then
b
∫ f(x) dH(x-s)=f(s) where H(x-s)=1 if x≧s
a 0 if x＜s
4 4 2
∫ x d[x]=∫ x d[x] - ∫ x d[x]
2 0 0
On [0,4] [x]=H(x-1)+H(x-2)+H(x-3)+H(x-4)
On [0,2] [x]=H(x-1)+H(x-2)
4 4 4 4 4
∫ x d[x] =∫ x dH(x-1) +∫ x dH(x-2) +∫ x dH(x-3) +∫ x dH(x-4)
0 0 0 0 0
=1+2+3+4=10
2
By the same method,we obtain ∫ x d[x]=1+2=3
0
4
Then ∫ x d[x] =10-3=7
2
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