In this subsection, $I = ]{-1,1}[$ and $w(x) = \frac{1}{\sqrt{1-x^2}}$. Show that, for every integer $k \in \mathbb{N}$, the function $x \mapsto x^k w(x)$ is integrable on $I$.
In this subsection, $I = ]{-1,1}[$ and $w(x) = \frac{1}{\sqrt{1-x^2}}$.
Show that, for every integer $k \in \mathbb{N}$, the function $x \mapsto x^k w(x)$ is integrable on $I$.