# 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** \({ a }^{ 2 }\) ??