TS EAMCET · Maths · Definite Integration
\(\int_0^{\frac{\pi}{2}} \sin ^6 \cdot x \cos ^4 \cdot x d x=\)
- A \(\frac{\pi}{256}\)
- B \(\frac{\pi}{512}\)
- C \(\frac{3\pi}{512}\)
- D \(\frac{5\pi}{512}\)
Answer & Solution
Correct Answer
(C) \(\frac{3\pi}{512}\)
Step-by-step Solution
Detailed explanation
\[ I=\int_0^{\pi / 2} \sin ^6 x \cos ^4 x d x \] Using Walli's Formula, \[ I=\frac{5 \times 3 \times 1 \times 3 \times 1}{10 \times 8 \times 6 \times 4 \times 2} \times \frac{\pi}{2}=\frac{3 \pi}{512} \]
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