If \({\rm{f}}\left( {\rm{x}} \right) = \frac{{2 - {\rm{xcos\;x}}}}{{2 + {\rm{xcos\;x}}}}\;\)and g(x) = loge x, (x > 0) then the value of the integral \(\mathop \smallint \limits_{ - \pi /4}^{{\rm{\pi }}/4} {\rm{g}}\left( {{\rm{f}}\left( {\rm{x}} \right)} \right){\rm{dx}}\) is:

If \({\rm{f}}\left( {\rm{x}} \right) = \frac{{2 - {\rm{xcos\;x}}}}{{2

1.	If \({\rm{f}}\left( {\rm{x}} \right) = \frac{{2 - {\rm{xcos\;x}}}}{{2 + {\rm{xcos\;x}}}}\;\)and g(x) = loge x, (x > 0) then the value of the integral \(\mathop \smallint \limits_{ - \pi /4}^{{\rm{\pi }}/4} {\rm{g}}\left( {{\rm{f}}\left( {\rm{x}} \right)} \right){\rm{dx}}\) is:
A.	log_e 3
B.	log_e e
C.	log_e 2
D.	log_e 1
Answer» E.

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If \({\rm{f}}\left( {\rm{x}} \right) = \frac{{2 - {\rm{xcos\;x}}}}{{2 + {\rm{xcos\;x}}}}\;\)and g(x) = loge x, (x > 0) then the value of the integral \(\mathop \smallint \limits_{ - \pi /4}^{{\rm{\pi }}/4} {\rm{g}}\left( {{\rm{f}}\left( {\rm{x}} \right)} \right){\rm{dx}}\) is:

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