No AM-GM here!

Calculus Level 5

$\large \displaystyle\int _{ 0 }^{ 2\pi }{ \sqrt { { a }^{ 2 }\sin ^{ 2 }{ x } +9\cos ^{ 2 }{ x } } } \, dx$

Over all constant real values of $a$ , what is the minimial value of the above expression?