9231 P11 - Nov 2011 - Q6 - 8 marks
6549
Let \(I_{n}=\int_{0}^{1} x^{n}(1-x)^{\frac{1}{2}} \mathrm{~d} x\), for \(n \geqslant 0\). Show that, for \(n \geqslant 1\),
\((3+2 n) I_{n}=2 n I_{n-1} .\)
Hence find the exact value of \(I_{3}\).
Solutions locked. Please sign in with access to view them.