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NDA 2013
Exam
NDA
Year
2013
Subject
Mathematics
Chapter
Definite Integration

NDA 2013 · Mathematics · Definite Integration

What is ∫_ (π)/(6) ^ (π)/(6) ( ^5 x ^3 x)/(x^4) d x is equal to?

What is ∫π6π6sin⁡5xcos⁡3xx4dx\int_{\frac{\pi}{6}}^{\frac{\pi}{6}} \frac{\sin ^5 x \cos ^3 x}{x^4} d x is equal to?

Options

  1. Aπ2\frac{\pi}{2}
  2. Bπ4\frac{\pi}{4}
  3. Cπ8\frac{\pi}{8}
  4. D00

Correct answer

D. 00

Step-by-step solution

∫π6π/6sin⁡5x⋅cos⁡3xx4dx=0(∵\int_{\frac{\pi}{6}}^{\pi / 6} \frac{\sin ^5 x \cdot \cos ^3 x}{x^4} d x=0 \quad(\because odd function ))
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