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प्रश्न
विकल्प
loge 3
- \[\log_e \sqrt{3}\]
- \[\frac{1}{2}\log\left( - 1 \right)\]
log (−1)
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उत्तर
\[\int_\frac{\pi}{6}^\frac{\pi}{3} \frac{1}{\sin2x} d x\]
\[ = \int_\frac{\pi}{6}^\frac{\pi}{3} \ cosec2x\ dx\]
\[ = \frac{1}{2} \int_\frac{\pi}{6}^\frac{\pi}{3} 2\ cosec2x\ dx\]
\[ = \frac{- 1}{2} \left[ \log\left( \ cosec\ 2x\ + \cot2x \right) \right]_\frac{\pi}{6}^\frac{\pi}{3} \]
\[ = \frac{- 1}{2}\left[ - 2\log\sqrt{3} \right]\]
\[ = \log\sqrt{3}\]
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