WBJEE · Maths · Definite Integration
\(\int_0^{2 \pi} \theta \sin ^6 \theta \cos \theta d \theta\) is equal to
- A \(\frac{\pi}{16}\)
- B \(\frac{3 \pi}{16}\)
- C \(\frac{16 \pi}{3}\)
- D 0
Answer & Solution
Correct Answer
(D) 0
Step-by-step Solution
Detailed explanation
Hint : Let \(I=\int_0^{2 \pi} \theta \sin ^6 \theta \cos \theta d \theta \ldots \ldots .(I)\) applying King's Property, \(\int_0^{2 \pi}(2 \pi-\theta) \sin ^6 \theta \cdot \cos \theta d \theta \ldots \ldots .(II)\) adding (I) and (II),…
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