Evaluate (1) ∫∫_D 1/√[(x-y)²+2(x+y)+1] dA (2)∫∫_D 1/√[(x+y)²+2(x-y)+1] dA,
where D={ (x,y) | 0 < x < 2, 0 < y < x }.
試求(1) ∫∫_D 1/√[(x-y)²+2(x+y)+1] dA (2)∫∫_D 1/√[(x+y)²+2(x-y)+1] dA,
其中D={ (x,y) | 0 < x < 2, 0 < y < x }.
A practice in double integral
2011-11-29 10:43 pm
回答 (2)
2011-12-03 4:59 pm
✔ 最佳答案
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參考資料：
my wisdom of maths + formula from http://en.wikipedia.org/wiki/List_of_integrals_of_irrational_functions
2011-12-02 10:10 pm
請參考!
答案: (1) 2ln2 - 0.5 (2) [5-√17+8ln(3+√17) - 8ln4 - ln(4+√17)]/4
作法: u=x+y, v=x-y
答案: (1) 2ln2 - 0.5 (2) [5-√17+8ln(3+√17) - 8ln4 - ln(4+√17)]/4
作法: u=x+y, v=x-y
收錄日期: 2021-05-04 00:57:07
原文連結 [永久失效]:
https://hk.answers.yahoo.com/question/index?qid=20111129000051KK00332