Let $n \in N$.
How to compare two integrals: $$ I_1=\int_0^{\infty}\left(\frac{\sin t}{t}\right)^n dt \quad \text{and} \quad I_2=\int_0^{\pi}\left(\frac{\sin t}{t}\right)^n dt\,\, ? $$
I've beet trying to compare them for some particular $n$. It seems, that $I_1>I_2$ for $n-\text{even}$ and $I_2>I_1$ for odd $n$.
Help me please to prove this statement for any $n\in N$.
Thank you.