AP EAMCET · Maths · Definite Integration
\(\int_0^\pi x \cdot \sin ^5 x \cdot \cos ^6 x d x=\)
- A \(\frac{16 \pi}{693}\)
- B \(\frac{8 \pi}{693}\)
- C \(\frac{4 \pi}{693}\)
- D \(\frac{2 \pi}{693}\)
Answer & Solution
Correct Answer
(B) \(\frac{8 \pi}{693}\)
Step-by-step Solution
Detailed explanation
\( \int_0^\pi x \cdot \sin^5 x \cdot \cos^6 x d x = \pi \int_0^{\pi/2} \sin^5 x \cdot \cos^6 x d x \) \( = \pi \cdot \frac{(5-1)!!(6-1)!!}{(5+6)!!} \) \( = \pi \cdot \frac{4!! \cdot 5!!}{11!!} \) \( = \pi \cdot \frac{8 \cdot 15}{10395} \)…
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