Minimize The Integral

Calculus Level 5

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 minimizes.

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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