Integrate y where
y=(x^2+1)^(1/2)
Please give presentation step by step. Thank you.
(20 marks)
Integration (AL) (20 marks)
2009-12-10 9:25 pm
回答 (1)
2009-12-11 4:10 am
✔ 最佳答案
Let x = sin@Then, dx = cos@d@
y = (x^2 + 1)^1/2
S y dx
= S (x^2 + 1)^1/2 dx
= S [sin^2@ + 1]^1/2 cos@ d@
= S (cos^2@)^1/2 cos@ d@
= S cos^2@ d@
= S [(1 + cos2@)/2] d@
= @/2 + sin2@ / 4 + C
= 1/2 arcsin x + 2sin@cos@ / 4 + C
= 1/2 arcsin x + x(1 - x^2)^1/2 / 2 + C
where C is a constant
參考: Physics king
收錄日期: 2021-04-19 20:47:48
原文連結 [永久失效]:
https://hk.answers.yahoo.com/question/index?qid=20091210000051KK00680