_ ^ ec x x 2 ;dx = - Vidyadip

MCQ

$\int_{}^{} {\frac{{\cos {\rm{ec}}x}}{{\log \tan \frac{x}{2}}}\;dx = } $

✓
$\log \left( {\log \tan \frac{x}{2}} \right) + c$
B
$2\log \left( {\log \tan \frac{x}{2}} \right) + c$
C
$\frac{1}{2}\log \left( {\log \tan \frac{x}{2}} \right) + c$
D
None of these

✓

Answer

Correct option: A.

$\log \left( {\log \tan \frac{x}{2}} \right) + c$

a
(a) $\log \tan \frac{x}{2} = t $ $ \Rightarrow \frac{1}{{\tan \frac{x}{2}}}.\frac{1}{2}{\sec ^2}\frac{x}{2}\,dx = dt$
$ \Rightarrow {\rm{cosec}}\,x\,dx = dt,$
therefore $\int_{}^{} {\frac{{{\rm{cosec}}\,x}}{{\log \tan \frac{x}{2}}}\,dx} = \int_{}^{} {\frac{1}{t}dt} = \log t + c = \log \left( {\log \tan \frac{x}{2}} \right) + c$.

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 - 7.1 inderfinite integral→STD 12 - 7.1 inderfinite integral — all question types→Mathematics STD 12 Science question papers→CBSE Board STD 12 Science question papers→CBSE Board question paper generator→

Similar questions

Objective function of a $\text{LPP}$ is:

If P and q are the order and degree of the differention $\text{y}\frac{\text{dy}}{\text{dx}}+\text{x}^{3}\frac{\text{d}^{2}\text{y}}{\text{dx}^{3}}+\text{xy}=\cos\text{x}$ then:

The distance between the planes $2x + 2y - z +2 = 0$ and $4x + 4y - 2z + 5 = 0$ is:

If $x = a \sec \theta, y = b \tan \theta$ then $\frac{d y}{d x}= ?$

If $y = {2^{1/{{\log }_x}4}}$, then $ x$ is equal to

If $\text{f(x)}=\begin{cases}\frac{\log(1+\text{ax})-\log(1-\text{bx})}{\text{x}},&\text{x}\neq0\\\text{k},&\text{x}=0\end{cases}$ and $f(x)$ is continous at $x = 0,$ then the value of $k$ is :

Let $f : R \rightarrow R$ be defined as,

$f(x)=\left\{\begin{array}{ll}-55 x, & \text { if } x<-5 \\ 2 x^{3}-3 x^{2}-120 x, & \text { if }-5 \leq x \leq 4 \\ 2 x^{3}-3 x^{2}-36 x-336, & \text { if } x>4\end{array}\right.$

Let $A=\{ x \in R : f$ is increasing $\} .$ Then $A$ is equal to :

The area of the region $S=\left\{(x, y): y^{2} \leq 8 x, y \geq \sqrt{2} x, x \geq 1\right\}$ is

If $\vec a,\vec b,\vec c$ are non- zero and non-coplanar vectors such that $\left( {\vec a + \lambda \vec b} \right).\left[ {\left( {\vec b + 3\vec c} \right) \times \left( {\vec c - 4\vec a} \right)} \right] = 0$ , then $\lambda $ is equal to

If $\text{V}=\frac{4}{3}\pi\text{r}^3,$ at What rate in cubic units is V increasing when $\text{r}=10\frac{\text{dr}}{\text{dt}}=0.01?$