CBSE Class 12-science Answered
intigrate w.r.t x
Asked by sumahr | 28 Dec, 2009, 07:44: PM
Expert Answer
Using sinx = 2sinx/2 cosx/2
and cosx = 2cos2x/2 - 1
f(x) = e-x/2(1-2sinx/2 cosx/2) / (2cos2x/2)
= e-x/2(sin2x/2 + cos2x/2 - 2sinx/2 cosx/2) / (2cos2x/2)
= e-x/2(sin2x/2 - cos2x/2)2 / (2cos2x/2)
= e-x/2(sinx/2 - cosx/2) / (2cos2x/2)
= e-x/2(tanx/2 secx/2 - secx/2)/2
f(x) dx = e-x/2(tanx/2 secx/2 - secx/2) dx/2
Put x/2 = y
=e-y(tany secy - secy) dy
= e-y tany secy dy - e-y secy dy
= e-y secy + e-y secy dy - e-y secy dy + c ......Integrating by parts, the first integral
= e-y secy + c
= e-x/2 secx/2 + c
Regards,
Team,
TopperLearning.
Answered by | 28 Dec, 2009, 10:36: PM
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