作者BaBi (迅雷不及掩耳盗铃)
看板trans_math
标题Re: [积分] 海洋大学101转学考
时间Tue Jun 25 00:04:37 2013
4 x^2
∫ ------------dx
0 √(2x+1)
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1F：→ yhliu:设 u=√(2x+1), x=(u^2-1)/2, 1≦u≦3 即可.111.252.122.112 06/24 22:41
Let u^2 = 2x+1, 2udu = 2dx , udu = dx
x = (u^2-1)/2 , x^2 = (1/4)(u^4-2u^2+1)
3
原式 = (1/4) ∫ (u^4-2u^2+1) du
1
|3
= (1/4) [ (u^5)/5 - (2u^3/3) + u ] |
|1
= 124/15
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