urgent integration help!!!

sonia11

New member
Joined
Oct 21, 2010
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2
I really need an urgent help on this question:

Integration of ( sin[x] ) ^ 3 / ( 1 + cos[x] ) ^ 4 dx from limit pi/4(lower limit) to pi/2 (upper limit).
I am really confused if we should take 1+cos[x] as the 'u' (substitution) or not because that completely changes the limit where upper limit becomes smaller than the lower limit.
Also when I am taking 1 - cos[x] (from sin^2 formula) as 'u' (substitution), then I am getting a very confusing value to integrate.
Any help for the problem will be highly highly appreciated.
Thanks in advance.
 
Use u = sin(x)1+cos(x) = tan(x/2). This yields,\displaystyle Use \ u \ = \ \frac{sin(x)}{1+cos(x)} \ = \ tan(x/2). \ This \ yields,

cos(x) = 1u21+u2, sin(x) = 2u1+u2, and\displaystyle cos(x) \ = \ \frac{1-u^2}{1+u^2}, \ sin(x) \ = \ \frac{2u}{1+u^2}, \ and

dx = 2du1+u2.\displaystyle dx \ = \ \frac{2du}{1+u^2}.

This will do it.\displaystyle This \ will \ do \ it.
 
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