$$f\left( x \right) = \left| {\matrix{
{\sec x} & {\cos x} & {{{\sec }^2}x + \cot x\cos ec\,x} \cr
{{{\cos }^2}x} & {{{\cos }^2}x} & {\cos e{c^2}x} \cr
1 & {{{\cos }^2}x} & {{{\cos }^2}x} \cr
} } \right|.$$
Then $$\int\limits_0^{\pi /2} {f\left( x \right)dx = .......} $$
Answer
$$ - \left( {{{15\pi + {{32}^ \circ }} \over {60}}} \right)$$