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