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AP EAMCET · Maths · Definite Integration

\[
\int_{-4 \pi}^{4 \pi} \tan ^9 x \sin ^6 x \cos ^3 x d x=
\]

  1. A \(16 \times \frac{\pi}{2}\)
  2. B \(8 \times \frac{2}{3}\)
  3. C \(16 \times \frac{14}{17} \times \frac{12}{15} \times \ldots \times \frac{2}{3}\)
  4. D 0
Verified Solution

Answer & Solution

Correct Answer

(D) 0

Step-by-step Solution

Detailed explanation

\begin{aligned} & \text {} \int_{-4 \pi}^{4 \pi} \tan ^9 x \sin ^6 x \cos ^3 x d x \\ & \text { here } f(x)=\tan ^9 x \sin ^6 x \cos ^3 x \\ & \Rightarrow f(-x)=[\tan (-x)]^9[\sin (-x)]^6[\cos (-x)]^3 \\ & \Rightarrow f(-x)=-\tan ^9 x \cdot \sin ^6 x \cos ^3 x=-f(x)…