\(\mathop \smallint \limits_{1/\pi }^{2/\pi } \frac{{\cos \left( {1/x} \right)}}{{{x^2}}}dx\)
\(\mathop \smallint \limits_{1/\pi }^{2/\pi } \frac{{\cos \left( {1/x} \right)}}{{{x^2}}}dx\; = \;\mathop \smallint \limits_{2/\pi }^{1/\pi } \frac{{ - \cos \left( {1/x} \right)}}{{{x^2}}}dx\)
\(= \;\mathop \smallint \limits_{\frac{\pi }{2}}^\pi {\rm{cosy}}dy\; = \;\left| {siny} \right|_{\pi /2}^\pi\)
= 0 - 1 = - 1
