推 kurt310452 :抱歉題目打錯了是-0.5次方 09/09 19:50
※ 引述《kurt310452 (憨 人)》之銘言：
: 1 x
: ∫∫ (x-1)*[(x+y)^(0.5)]dydx
: 0 0
1
=∫ (x-1) 2/3(x+y)^(1.5)|y={0~x} dx
0
1
=∫ (x-1) 2(2^(1.5)-1)/3 x^(1.5) dx
0
1
= 2(2^(1.5)-1)/3 ∫ (x^(2.5) - x^(1.5)) dx
0
= 2(2^(1.5)-1)/3 (2/7- 2/5)
= -8(2^(1.5)-1)/105
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