intigrate w.r.t x

Asked by sumahr | 9th Jan, 2010, 08:38: PM

Expert Answer:

(sin2x+cos2x)2 = sin4x+2sin2xcos2x+cos4x

1-2sin2xcos2x = sin4x+cos4x

sin4x+cos4x = 1-2(1-cos2x)cos2x = 1-2cos2x+2cos4

f(x) = (sin2x)/(1-sin22x /2)

= 2 sin2x/(1+cos22x)

Now put cos2x = y,  sin2x dx = -dy/2 and x = 0 y = 1; x = π/2 y = -1

f(y) = -dy/(2(1+y2))

Integrating we find,

-(1/2)tan-1y

And using the limits,

(-1/2)(-π/4 - π/4)

= π/4

Regards,

Team,

TopperLearning.

 

 

 

 

 

Answered by  | 10th Jan, 2010, 12:20: AM

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