Taking <i>q</i>(<i>x</i>)=1, <i>q</i>(<i>x</i>)=<i>x</i>
and <i>q</i>(<i>x</i>)=<i>x</i><sup>2</sup> in equation (1) and working out
the integral (easy!) will give you three
equations which you can solve to find
&#955;<sub>1</sub>,&#x00A0;&#955;<sub>2</sub> and &#955;<sub>3</sub>.
<p/>
The key to showing that the same formula works
for other polynomials is to show that if it works
for 1,&#x00A0;<i>x</i> and <i>x</i><sup>2</sup> it works for any linear
combination of them and so for any quadratic
polynomial.
<p/>
Finally you can go on to check out the formula
for <i>x</i><sup>3</sup>,&#x00A0;<i>x</i><sup>4</sup> and <i>x</i><sup>5</sup>.