Simple Integration

👨🏻‍🏫 學術台數學

John

2009-08-11 5:52 am

一時間唔記得點 integrate:

x / squareroot(1-x^2)

要 steps / 方法, thx

回答 (2)

STEVIE-G™

2009-08-11 6:05 am

✔ 最佳答案

As follows:

圖片參考：http://i707.photobucket.com/albums/ww74/stevieg90/02-47.gif

(http://i707.photobucket.com/albums/ww74/stevieg90/02-47.gif)

2009-08-10 23:41:44 補充：
yes...再補充一下石石個做法:
Let u=1-x^2 , then du=-2xdx

∫x/√(1-x^2) dx
=∫x/√u (du/-2x)
=-1/2∫du/√u
=-1/2 (2√u)+c
=-√u+c
=-√(1-x^2)+c

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石石

2009-08-11 7:27 am

or, you can set a variable u to be 1-x^2,
and this method is called "Substitution".

Stevie-G's method is an advanced substitution method

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