int_{pi /6}^{pi /4} text{cosec} , 2x , dx = | vedclass

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Question

(D) We know that $\int 	ext{cosec} \, ax \, dx = \frac{1}{a} \log |	an(\frac{ax}{2})| + C$. Applying this to the given integral: $\int_{\pi /6}^{\pi

Vedclass · Accepted Answer

$\frac{1}{2} \log \sqrt{3}$

Vedclass · Answer

(D) We know that $\int 	ext{cosec} \, ax \, dx = \frac{1}{a} \log |	an(\frac{ax}{2})| + C$. Applying this to the given integral: $\int_{\pi /6}^{\pi /4} 	ext{cosec} \, 2x \, dx = \left[ \frac{1}{2} \log |	an(\frac{2x}{2})| ight]_{\pi /6}^{\pi /4}$ $= \frac{1}{2} [\log 	an x]_{\pi /6}^{\pi /4}$ $= \frac{1}{2} [\log 	an(\frac{\pi}{4}) - \log 	an(\frac{\pi}{6})]$ $= \frac{1}{2} [\log(1) - \log(\frac{1}{\sqrt{3}})]$ $= \frac{1}{2} [0 - \log(3^{-1/2})]$ $= \frac{1}{2} [\frac{1}{2} \log 3] = \frac{1}{4} \log 3 = \frac{1}{2} \log \sqrt{3}$.

$\int_{\pi /6}^{\pi /4} \text{cosec} \, 2x \, dx = $

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