If I_ n = ^ n x d x then I_ n - ( n-1 n ) I_ n-2 =
Mathematics · JEE Advanced · NTA Exams — Integral Calculus
If \(I_{n}=\int \cos ^{n} x d x\)then \(I_{n}-\left(\frac{n-1}{n}\right) I_{n-2}\)=
- cosn–1 x . sin x + c
- \(\frac{1}{n}\left(\cos ^{n-1} x \sin x\right)+c\)
- \(\frac{1}{n}\left(\cos ^{n} x \sin x\right)+c\)
- None of these
Answer
(B) 1 n ( ^ n-1 x x )+c
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