intigrate w.r.t x

Asked by sumahr | 28th 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  | 28th Dec, 2009, 10:36: PM

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