Elementary evaluation of ${\int }_0^{\mathrm{\infty }}si{n}^{p}t\mathrm{/}{t}^{q}dt$

Let $p$ and $q$ be two positive integers, the goal of this note is to demonstrate, in a very simple and elementary way without using advanced tools, a formula to express the value of the integral $I(p,q)=\int_0^\infty{\sin^p t\over t^q}dt$ when it converges.