(x-[x])²dx
範圍是從-3~3,要算積分,[ ]是高斯符號
麻煩高手解答,感謝!
更新1:
對了,麻煩要解釋計算過程,謝謝
一題微積分問題(有高斯符號)?
回答 (2)
2017-12-18 7:13 am
✔ 最佳答案
Soln<=x<n+1，n為整數
[x]=n
x－[x]=x－n
A=∫(n to n+1)_(x－[x])^2dx
=∫(n to n+1)_(x－n)^2dx
Set y=x－n
A=∫(0 to 1)_y^2dy=1/3
So
∫(－3 to 3)_(x－[x])^2dx
=(1/3)*6
=2
2017-12-17 11:09 pm
當 x<0
(x-[x])²=[x-(-x)]^2=(2x)²=4x²
當 0≤x
(x-[x])²=0
所求=(x-[x])²dx 範圍是從-3~0
=4x² dx 範圍是從-3~0
= (4/3) x^3 範圍是從-3~0
= (4/3)*3^3
= 36
(x-[x])²=[x-(-x)]^2=(2x)²=4x²
當 0≤x
(x-[x])²=0
所求=(x-[x])²dx 範圍是從-3~0
=4x² dx 範圍是從-3~0
= (4/3) x^3 範圍是從-3~0
= (4/3)*3^3
= 36
收錄日期: 2021-04-30 22:34:58
原文連結 [永久失效]:
https://hk.answers.yahoo.com/question/index?qid=20171217140329AAl8jFP