作者Frobenius (i^(-i)= e^(π/2))
看板trans_math
标题Re: [考古] 重积分
时间Wed Dec 27 18:39:09 2006
※ 引述《GayerDior (最近色团越来越忙o(＞＜:)》之铭言：
: E:[83交大]
: Let R ={ (x，y)|(x-1)^2 + (y-1)^2 ≦ 2 }. Fill the following blanks:
1+√2 1+√(1+2y-y^2)
╴╴╴ ╴╴╴╴╴╴╴ √(x^2+y^2)
∫∫ √(x^2+y^2) dxdy = ∫ ∫ ╴╴╴╴╴╴ dxdy
R 1-√2 1-√(1+2y-y^2)
╴╴╴ ╴╴╴╴╴╴╴
2π √2
╴╴╴ ╴╴╴ r
= ∫ ∫ ╴╴╴╴ r drdΘ
0 0
╴╴╴ ╴╴╴
2π r^3 |r = √2
= ∫ (-----)| dΘ
0 3 |r = 0
2π 2√2
= ∫ (----) dΘ
0 3
4√2
----π
3
= ╴╴╴╴╴╴
: 如果有人会写，
: 帮我写出详细过程，不要只填空格
: 拜托了，谢谢
(x-1)^2 + (y-1)^2 = 2 => x = 1 ± √(1+2y-y^2)
(1-1)^2 + (y-1)^2 = 2 => y = 1 ± √2
╴╴╴╴╴╴╴╴╴╴╴╴
√(x^2+y^2) = √(rCosΘ)^2 + (rSinΘ)^2 = r
dxdy = rdrdΘ
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