A calculus problem by Vighnesh Raut

Calculus Level 3

Let \[\displaystyle{f\left( x \right) =\int _{ \frac { { \pi }^{ 2 } }{ 16 } }^{ { x }^{ 2 } }{ \frac { \cos { x } \cos { \sqrt { \theta } } }{ 1+\sin ^{ 2 }{ \sqrt { \theta } } } d\theta } }\]

Find 'k' if \[f'(\pi )=\frac { 2\pi }{ k } \]

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