Edexcel FP2 2020 June — Question 7

Exam BoardEdexcel
ModuleFP2 (Further Pure Mathematics 2)
Year2020
SessionJune
TopicIntegration by Parts
7. $$I _ { n } = \int \left( 4 - x ^ { 2 } \right) ^ { - n } \mathrm {~d} x \quad n > 0$$
  1. Show that, for \(n > 0\) $$I _ { n + 1 } = \frac { x } { 8 n \left( 4 - x ^ { 2 } \right) ^ { n } } + \frac { 2 n - 1 } { 8 n } I _ { n }$$
  2. Find \(I _ { 2 }\)
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