Re: 一題積分
Key:同乘√(1+sin x)
4 pi 4
pi cos x cos x √(1+sin x)
∫ ----------- dx = ∫ -------------------- dx
√(1-sin x) √(1-sin x)(1+sin x)
5pi/6 5pi/6
pi 4
cos x √(1+sin x) 2 2
= ∫------------------- dx (by sin x + cos x = 1)
5pi/6 |cos x|
pi 3
= -∫ cos x√(1+sin x)dx (since cos x < 0 for x
5pi/6 in [5pi/6, pi] )
pi 2
= -∫ cos x√(1+sin x) cosx dx
5pi/6
pi 2
= -∫ (1-sin x) √(1+sin x) cosx dx
5pi/6
1 2
= -∫ [1-(u-1) ]√u du
3/2
1 3/2 5/2
= -∫ (2u - u ) du
3/2
7/2 5/2 1
= (2/7 u -4/5 u ) |
3/2
5/2
= -18/35 + 13/35(3/2)
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※ 編輯: yueayase (220.129.21.68), 08/16/2014 22:33:20
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