state whether you would use integration by parts to evalute the integral Sx(x+4)^1/2dx if so ,identify u and solve the problem.
看不太懂題目的意思??要怎麼做?
一題積分運算~~天助幫幫忙
2010-06-26 9:31 am
回答 (3)
2010-06-26 9:52 am
✔ 最佳答案
integration by parts: ∫udv=uv-∫vdu(A)=∫ x√(x+4) dx
u=x , dv=√(x+4)dx
du=dx, v=(2/3)(x+4)^(3/2)
so, (A)= x*(2/3)(x+4)^(3/2) - (2/3) ∫(x+4)^(3/2) dx
=(2x/3)(x+4)^(3/2)-(2/3)*(2/5)(x+4)^(5/2) +C
=(2x/3)(x+4)^(3/2)-(4/15) (x+4)^(5/2) + C
2010-06-26 08:57:41 補充：
題目:若用分部積分法,請分辨u為何?
rex大直接用代換積分法,當然也行!
2010-06-26 08:58:35 補充：
指名作答,是對他人的不尊重,請勿再為之!
2010-06-26 6:04 pm
令u=x+4...............................(其餘自行想像)
2010-06-26 12:20 pm
哇 天助有人指名叫檯耶~~~
2010-06-26 04:20:02 補充：
我來陪檯了
一般是令根號裡的為u, u=√(x+4), x=u^2-4-->dx=2udu
∫x√(x+4) dx
=∫(u^2-4)*u 2udu
=∫(2u^4-8u^2) du
=(2/5)u^5-(8/3)u^3
=(2/5)(x+4)^(5/2)-(8/3)(x+4)^(3/2)+C
2010-06-26 04:20:02 補充：
我來陪檯了
一般是令根號裡的為u, u=√(x+4), x=u^2-4-->dx=2udu
∫x√(x+4) dx
=∫(u^2-4)*u 2udu
=∫(2u^4-8u^2) du
=(2/5)u^5-(8/3)u^3
=(2/5)(x+4)^(5/2)-(8/3)(x+4)^(3/2)+C
收錄日期: 2021-04-30 15:00:29
原文連結 [永久失效]:
https://hk.answers.yahoo.com/question/index?qid=20100626000010KK00660