WBJEE · Maths · Indefinite Integration
If \(I_n=\int_0^{\frac{\pi}{2}} \cos ^n x \cos n x d x\), then \(I_1, I_2, I_3 \ldots\) are in
- A A.P.
- B G.P.
- C H.P
- D no such relation
Answer & Solution
Correct Answer
(B) G.P.
Step-by-step Solution
Detailed explanation
Hint : \(I_n=\int_0^{\pi / 2} \cos ^n x \cdot \cos n x d x\) \(I_1=\int_0^{\pi / 2} \cos x \cdot \cos x d x=\int_0^{\pi / 2}\left(\frac{1+\cos 2 x}{2}\right) d x=\frac{\pi}{4}\) \(I_2=\int_0^{\pi / 2} \cos ^2 x \cdot \cos 2 x d x=\int_0^{\pi / 2}-\sin ^2 x \cdot \cos 2 x d x\)…
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