Suppose that f(x)=ln( 2sin²x + 3cos²x),
evaluate the definite integral of f(x) from x=0 to x=π.
evaluate the integral
2012-04-24 6:19 pm
回答 (2)
2012-04-26 2:59 am
2012-04-26 5:26 pm
對 g(0) 之求法，我補充一下：
觀察∫_{0→(π/2)} ln[cos(x)] dx
= ∫_{0→(π/2)} ln[sin(x)] dx
令其值為 I。
即得
2I
= ∫_{0→(π/2)} ln[(sin(x) cos(x)] dx
= -(π/2) ln(2) + (1/2)∫_{0→π)} ln[sin(u)]} du
｛letting u = 2x)
= -(π/2) ln(2) + I
即得 I = -(π/2) ln(2)
觀察∫_{0→(π/2)} ln[cos(x)] dx
= ∫_{0→(π/2)} ln[sin(x)] dx
令其值為 I。
即得
2I
= ∫_{0→(π/2)} ln[(sin(x) cos(x)] dx
= -(π/2) ln(2) + (1/2)∫_{0→π)} ln[sin(u)]} du
｛letting u = 2x)
= -(π/2) ln(2) + I
即得 I = -(π/2) ln(2)
收錄日期: 2021-04-23 23:24:47
原文連結 [永久失效]:
https://hk.answers.yahoo.com/question/index?qid=20120424000051KK00143