Consider an Integral

$I\quad =\quad \int _{ 0 }^{ { \pi }/{ 2 } }{ \left| \cos { x } -kx \right| } dx.$

If for some **positive Real** value of **k** this integral can be **minimized**.

if that value of **k** is expressed as

$\quad \cfrac { \sqrt { a } }{ \pi } (\cos { (\cfrac { \pi }{ \sqrt { a } } ) } ).$

**Then Find** ${ a }^{ 2 }$ ??

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