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

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

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 = $

Similar Questions

If $\int_{1}^{2} \frac{dx}{(x^2 - 2x + 4)^{3/2}} = \frac{k}{k+5}$,then $k$ is equal to

$\int_{0}^{4}|x-2| d x=$

$\int_0^1 \sin \left(2 \tan ^{-1} \sqrt{\frac{1+x}{1-x}}\right) d x$ is equal to :

What is the value of $\int \limits_0^1 \cos (\pi x) \cos ([2 x] \pi) d x$? (Here $[t]$ denotes the greatest integer function of the real number $t$.)

The value of $\int_{0}^{\sqrt{2}} [x^2] \, dx$,where $[.]$ denotes the greatest integer function.

Vedclass Test Series

Exam Paper Generator

Online Exam Module