A-LevelFurther MathematicsIntegration9231/12 · May/June 2019 · Q48 Marks
It is given that, for n ≥ 0, In = ∫0^1 xⁿe^(x³) dx.
- (i)Show that I₂ = ⅓(e – 1).[2]
- (ii)Show that, for n ≥ 3, 3Iₙ = e - (n-2)Iₙ₋₃.[3]
- (iii)Hence find the exact value of I₈.[3]
Mark scheme
Marking points from the official mark scheme (May/June 2019). The mark or mark type is shown in brackets.
- [2] Must show working, AG.
- [2] Integrates by parts. AG
- [1] AG
- [2] Applies reduction formula once and uses (i).
- [1] Must be exact.
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