Let I_n = ∫ (from 0 to ½π) xⁿ sin x dx.
- (i)Prove that, for n ≥ 2, I_n + n(n − 1)I_{n-2} = n(½π)ⁿ⁻¹.[4]
- (ii)Calculate the exact value of I₁ and deduce the exact value of I₃.[3]
Mark scheme
Marking points from the official mark scheme (May/June 2017). The mark or mark type is shown in brackets.
- [M1A1] Uses integration by parts with u = x^n
- [A1]
- [A1] (AG)
- [M1]
- [A1]
- [B1 FT]
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