Minimize The Integral

Calculus Level 5

Consider an Integral

I=0π/2cosxkxdx.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

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

Then Find a2{ a }^{ 2 } ??

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