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TS EAMCET · Maths · Definite Integration

\(\int_{-2 \pi}^{2 \pi} \sin ^4 x \cos ^6 x d x=\)

  1. A \(\frac{3 \pi}{128}\)
  2. B \(\frac{9 \pi}{32}\)
  3. C \(\frac{9 \pi}{64}\)
  4. D \(\frac{3 \pi}{64}\)
Verified Solution

Answer & Solution

Correct Answer

(D) \(\frac{3 \pi}{64}\)

Step-by-step Solution

Detailed explanation

\( = 2 \int_{0}^{2 \pi} \sin ^4 x \cos ^6 x d x \) \( = 4 \int_{0}^{\pi} \sin ^4 x \cos ^6 x d x \) \( = 8 \int_{0}^{\pi/2} \sin ^4 x \cos ^6 x d x \) \( = 8 \left( \frac{(4-1)!! (6-1)!!}{(4+6)!!} \cdot \frac{\pi}{2} \right) \)…