CBSE Class 12-science Answered
intigrate w.r.t x
Asked by sumahr | 09 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+2cos4x
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 | 10 Jan, 2010, 12:20: AM
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