Re: [考古] 93成大
※ 引述《dodo1654 (secret)》之銘言：
: 2
: 3.設集合Ｓ為由曲線ｙ=|x-1|與2y=ｘ -2x+2所圍之區域
y = (1/2)[(x-1)^2+1]
2 (1/2)[(x-1)^2+1]
S = 2∫ ∫ dy dx
1 x-1
1
= ∫ [u^2 - 2u + 1]du u = x-1
0
= 1/3 - 1 + 1 = 1/3
: (b)試求函數f(x,y)=y在集合Ｓ上之二重積分。
2 (1/2)[(x-1)^2+1]
S = 2∫ ∫ y dy dx
1 x-1
2
= ∫ [(1/4)[(x-1)^2 +1]^2 - (x-1)^2] dx
1
1
= ∫ (1/4)[u^4 + 2u^2 + 1 - 4u^2]du
0
1
= ∫ (1/4)[u^4 - 2u^2 + 1]du
0
= (1/4)[1/5 - 2/3 + 1]
= 2/15
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◆ From: 122.124.99.94
※ 編輯: Honor1984 來自: 122.124.99.94 (07/11 02:17)
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