calculus - Evaluate $limlimits_{x to infty } {left( {int_0^{pi /6} {{{(sin t)}^x}dt} } right)^{1/x}}$

It is given that the following limit
$\mathop {\lim }\limits_{x \to \infty } {\left( {\int\limits_0^{\pi /6} {{{(\sin t)}^x}dt} } \right)^{1/x}}$ exists. Evaluate the limit.

I've tried tackling this problem but I can't seem to get started. Any hint is appreciated, thanks!