TS EAMCET · Maths · Indefinite Integration
If \(I_n=\int \cos ^n x d x\), then \(6 I_6-5 I_4=\)
- A \(-\cos ^5 x \sin ^2 x\)
- B \(\cos ^6 x \sin ^2 x\)
- C \(\cos ^3 x \sin ^2 x\)
- D \(\cos ^5 x \sin x\)
Answer & Solution
Correct Answer
(D) \(\cos ^5 x \sin x\)
Step-by-step Solution
Detailed explanation
\begin{aligned} & I_n=\int \cos ^n x d x \\ & =\int \cos ^{n t-1} x \cdot \cos x d x \\ & =\cos ^{n t-1} x \cdot \sin x-\int(n-1) \cos ^{n t-2} x \\ & (-\sin x) \cdot(\sin x) d x \\ & =\cos ^{n t-1} x \sin x+\int \cos ^{n t-2} x \cdot(n-1) \sin ^2 x d x \\ & =\cos ^{n+1} x \sin…
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