_ /6 ^ /4 cosec ,2x ,dx = - Vidyadip

MCQ

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

A
$\log 3$
B
$\log \sqrt 3 $
C
$\log 9$
✓
$\frac{1}{2}\log \sqrt 3 $

✓

Answer

Correct option: D.

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

d
(d) $\int_{\pi /6}^{\pi /4} {{\rm{cosec}}\,2x\,dx} = \frac{1}{2}[\log \tan x]_{\pi /6}^{\pi /4}$

$ = \frac{1}{2}\left[ {\log \tan \frac{\pi }{4} - \log \tan \frac{\pi }{6}} \right] = \frac{1}{2}\log \sqrt 3 $.

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Explore more

More "M.C.Q (1 Marks)" from STD 12 - 7.2 definite integral→STD 12 - 7.2 definite integral — all question types→Mathematics STD 12 Science question papers→CBSE Board STD 12 Science question papers→CBSE Board question paper generator→

Similar questions

The value of $\int \cos ^2 x\ d x$ will be

Let $f:\left[ {0,2} \right] \to R$ be a twice differentiable function such that $f''\left( x \right) > 0$, for all $x \in \left( {0,2} \right)$. If $\phi \left( x \right) = f\left( x \right) + f\left( {2 - x} \right)$, then $\phi $ is

The number of arbitrary constants in the general solution of a differential equation of fourth order are:

Choose the correct answer from the given four options. If $\text{A}=\frac{1}{\pi}\begin{bmatrix}\sin^{-1}(\text{x}\pi)&\tan^{-1}\Big(\frac{\text{x}}{\pi}\Big)\\\sin^{-1}\Big(\frac{\text{x}}{\pi}\Big)&\cot^{-1}(\pi\text{x})\end{bmatrix}$ and $\text{B}=\frac{1}{\pi}\begin{bmatrix}-\cos^{-1}(\text{x}\pi)&\tan^{-1}\Big(\frac{\text{x}}{\pi}\Big)\\\sin^{-1}\Big(\frac{\text{x}}{\pi}\Big)&\tan^{-1}(\pi\text{x})\end{bmatrix}$ then $A - B$ is :

Let three points $A(2,3,4), B(3,4,2)$ and $C(4,2,3)$ in space are given. A point $D$ in space is such that it is at a distance of $\sqrt 6$ units from $3$ given points. Then volume of tetrahedron $ABCD$ is -

$\int_{}^{} {\frac{1}{x}\log x\;dx} $ is equal to

An integrating factor of the differential equation $\frac{{dy}}{{dx}} + \frac{{2xy}}{{1 - {x^2}}} = \frac{x}{{\sqrt {1 - {x^2}} }}$ is

A die is tossed thrice. If getting a four is considered a success, then the mean and variance of the probability distribution of the number of successes are

Suppose the limit $L=\lim _{n \rightarrow \infty} \sqrt{n} \int_0^1 \frac{1}{\left(1+x^2\right)^n} d x$ exists and is larger than $\frac{1}{2}$. Then,

The order of differential equation $\frac{\text{d}^2\text{y}}{\text{dx}^2}-\Big(\frac{\text{dy}}{\text{dx}^2}\Big)=1$ is: