Definite Integral

2012-05-24 3:01 am
Find ∫ x sin x /(1 + e^x) dx from x = - π/2 to x = π/2
更新1:

Answer is 1.

回答 (2)

2012-05-24 3:17 am
✔ 最佳答案
∫_[-π/2~0] x sinx/(1+e^x) dx +∫_[0~π/2] x sinx/(1+e^x)dx
=∫_[π/2~0] -xsin(-x)/[1+e^(-x)] (-dx)+ ∫_[0~π/2] xsinx/(1+e^x) dx
=∫_[0~π/2] xsinx e^x/(e^x+1) dx +∫_[0~π/2] xsinx/(1+e^x)dx
=∫_[0~π/2] xsinx dx
= -xcosx+ sinx for x=0~π/2
= 1
2012-05-24 4:10 pm
媽弗勒時﹗媽弗勒時﹗

2012-05-24 08:10:17 補充:
媽弗勒時﹗媽弗勒時﹗


收錄日期: 2021-04-28 14:21:06
原文連結 [永久失效]:
https://hk.answers.yahoo.com/question/index?qid=20120523000051KK00473

檢視 Wayback Machine 備份