Cengupe Lewney

Auignamers $-2102$ section $-0$

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$8.[8/13$ Points$]$

Verify by direct integration that the functions are orthogonal with respect to the indicated weight function $w(x)$ on the given interval.

$t_0[x]=1,t_1[x]=-x1,t_2(x)=\frac{1}{2}{x}^2-2x1$

$w(x)=e^{-x},[0,-x)$

Using integration by parts we find the following. $($in the last step of each antegral, sumply your anyer completelf.$)$