$$\[ I_{n}=\int_{0}^{k} x^{n}(k-x)^{\frac{1}{2}} \mathrm{~d} x \quad n \geqslant 0 \]$$ where $$\(k\)$$ is a positive constant. Show that $$\[ I_{n}=\frac{2 k n}{3+2 n} I_{n-1} \quad n \geqslant 1 \]$$ (5)

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