How to calculate \frac{I_{n+2}}{I_n} of I_n=\int_{\frac {-\pi}{2}}^\frac{\pi}{2} \cos^n \theta d\theta I

occhei042

occhei042

Answered question

2022-04-22

How to calculate In+2In of In=π2π2cosnθdθ
I could calculate that nIn=2cosn1θsinθ+2(n1)0π2In2dθ but how do I caluclate the In+2?

Answer & Explanation

drenkttj9

drenkttj9

Beginner2022-04-23Added 20 answers

Correction: you meant nIn=[cosn1θsinθ]π2π2+(n1)(In2In). The first term vanishes if n2 because cos±π2=0

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