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Year 12 Maths Extension 2 Integration

Recurrence Relations

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Questions
Question 1
35329

i) If \({I_n} = \int\limits_0^{\pi /4} {{{\tan }^n}x\,\,dx} \), show that \({I_n} + {I_{n - 2}} = \dfrac{1}{{n - 1}}\).

ii) Hence evaluate \({I_5}\)

i) True ii) \({I_5} = \dfrac{1}{4}(\log 4 - 1)\)

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