想問點樣用INTEGRATION BY PARTS做以下兩條
1.in sin^2(x)
2.in cos^2(x)
小弟自修數學的,
冇讀過PURE
所以唔太明
謝解答
integration by parts
2012-06-26 11:06 pm
回答 (4)
2012-06-27 12:00 am
✔ 最佳答案
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2012-06-26 23:04:25 補充：
∫ sin^2 x dx = [x - (sin 2x)/2] + C
∫ cos^2 x dx = [x + (sin 2x)/2] + C
參考: 原創答案
2012-06-27 8:34 am
constant term is useless in this case
2012-06-27 6:38 am
stupid question: constant term (+C) is not required?
2012-06-27 13:44:18 補充：
further explanation plz ?
2012-06-27 13:44:18 補充：
further explanation plz ?
2012-06-26 11:14 pm
We usually don't integrate sin²x & cos²x by part.
By using the fact that:
sin²x = (1/2)(1 - cos 2x) & cos²x = (1/2)(1 + cos 2x)
We can get:
∫sin²x dx = (1/2)(x - (1/2)sin 2x) & ∫sin²x dx = (1/2)(x + (1/2)sin 2x)
By using the fact that:
sin²x = (1/2)(1 - cos 2x) & cos²x = (1/2)(1 + cos 2x)
We can get:
∫sin²x dx = (1/2)(x - (1/2)sin 2x) & ∫sin²x dx = (1/2)(x + (1/2)sin 2x)
收錄日期: 2021-04-13 18:46:45
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