AP EAMCET · Maths · Indefinite Integration
\(\int \sin ^5 x \cdot \cos ^5 x d x=\)
- A \(\frac{\cos ^6 x}{60}\left(6 \sin ^4 x+3 \sin ^2 x+1\right)+c\)
- B \(-\frac{\sin ^6 x}{60}\left(6 \cos ^4 x+3 \cos ^2 x+1\right)+c\)
- C \(-\frac{\cos ^6 x}{60}\left(6 \sin ^4 x+3 \sin ^2 x+1\right)+c\)
- D \(\frac{\sin ^6 x}{60}\left(6 \cos ^4 x+3 \cos ^2 x+1\right)+c\)
Answer & Solution
Correct Answer
(C) \(-\frac{\cos ^6 x}{60}\left(6 \sin ^4 x+3 \sin ^2 x+1\right)+c\)
Step-by-step Solution
Detailed explanation
\[ \begin{aligned} I & =\int \sin ^5 x \cos ^5 x d x \\ & =\int \cos ^5 x \sin ^4 x \sin x d x \\ & =\int \cos ^5 x\left(1-\cos ^2 x\right)^2 \sin x d x \end{aligned} \] Let \(\cos x=t \Rightarrow-\sin x d x=d t\)…
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