9231 P21 - Jun 2025 - Q2 - 7 marks
5904
Let \(I_{n}=\int_{0}^{1}(1-x)^{n} \sinh x \mathrm{~d} x\), where \(n\) is a non-negative integer.
(a) Show that, for \(n \geqslant 2, \quad I_{n}=-1+n(n-1) I_{n-2}\).
(b) Find the exact value of \(I_{2}\).
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