_ ^ dx (2 x + x) ^2 = - Vidyadip

MCQ

$\int_{}^{} {\frac{{dx}}{{{{(2\sin x + \cos x)}^2}}}} = $

A
$\frac{1}{2}\left( {\frac{1}{{2\tan x + 1}}} \right) + c$
B
$\frac{1}{2}\log (2\tan x + 1) + c$
✓
$\frac{1}{{2 + \cot x}} + c$
D
$ - \frac{1}{2}\left( {\frac{1}{{2\tan x - 1}}} \right) + c$

✓

Answer

Correct option: C.

$\frac{1}{{2 + \cot x}} + c$

c
(c) $\int_{}^{} {\frac{{dx}}{{{{(2\sin x + \cos x)}^2}}} = \int_{}^{} {\frac{{dx}}{{{{\sin }^2}x{{(2 + \cot x)}^2}}}} } = \int_{}^{} {\frac{{{\rm{cose}}{{\rm{c}}^{\rm{2}}}x\,dx}}{{{{(2 + \cot x)}^2}}}} $
Put $(2 + \cot x) = t \Rightarrow - {\rm{cose}}{{\rm{c}}^{\rm{2}}}x\,dx = dt$
$ = \int_{}^{} {\frac{{ - dt}}{{{t^2}}}} = \frac{1}{t} + c = \frac{1}{{2 + \cot x}} + 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 7.1 inderfinite integral→7.1 inderfinite integral — all question types→Maths STD 12 Science question papers→Gujarat Board STD 12 Science question papers→Gujarat Board question paper generator→

Similar questions

Let A = {1, 2, ......., n} and B = {a, b}. Then the number of subjections from A into B is:

$^{\text{n}}\text{P}_2$
$2^\text{n}-2$
$2^\text{n}-1$
$^{\text{n}}\text{C}_2$

The total number of matrices formed with the help of 6 different numbers are:

6
6!
2(6!)
4(6!)

Consider the matrices $A =$ $\left[ {\begin{array}{*{20}{c}}4&6&{ - 1}\\3&0&2\\1&{ - 2}&5\end{array}} \right]$ , $B =$ $\left[ {\begin{array}{*{20}{c}}2&4\\0&1\\{ - 1}&2\end{array}} \right]$ , $C =$ $\left[{\begin{array}{*{20}{c}}3\\1\\2\end{array}} \right]$ . Out of the given matrix products
$(i)$ $(AB)^TC$ $(ii)$ $C^TC(AB)^T$ $(iii)$ $C^TAB$ and $(iv)$ $A^TABB^TC$

If A is a matrix of order 3 and |A| = 8, then |adj A| =

1
2
2³
2⁶

Consider the binary operation × on Q defind by a × b = a + 12b + ab for a, b ∈ Q. Find $2\times\frac{1}{3}$

$\frac{20}{3}$
4
18
$\frac{16}{3}$

if x lies in the interval [0, 1], then the least value of x² + x + 1 is :

$3$
$\frac{3}{4}$
$1$
none of these.

Let $\mathrm{A}=\{1,2,3,4,5\}$. Let $\mathrm{R}$ be a relation on $\mathrm{A}$ defined by $x R y$ if and only if $4 x \leq 5 y$. Let $m$ be the number of elements in $\mathrm{R}$ and $\mathrm{n}$ be the minimum number of elements from $\mathrm{A} \times \mathrm{A}$ that are required to be added to $\mathrm{R}$ to make it a symmetric relation. Then $m+n$ is equal to:

If $y = a\log |x| + b{x^2} + x$ has its extremum values at $x = - 1$ and $x = 2$, then

A company has two plants $\mathrm{A}$ and $\mathrm{B}$ to manufacture motorcycles. $60 \%$ motorcycles are manufactured at plant $\mathrm{A}$ and the remaining are manufactured at plant B. $80 \%$ of the motorcycles manufactured at plant $\mathrm{A}$ are rated of the standard quality, while $90 \%$ of the motorcycles manufactured at plant $B$ are rated of the standard quality. A motorcycle picked up randomly from the total production is found to be of the standard quality. If $p$ is the probability that it was manufactured at plant $\mathrm{B}$, then $126 \mathrm{p}$ is

The differention equation $\frac{\text{dy}}{\text{dx}}+\text{P}\text{y}=\text{Qy}^{\text{n}},\text{n}>2$ can be reduced to linear from by substituting:

$\text{z}=\text{y}^{\text{n}-1}$
$\text{z}=\text{y}^{\text{n}}$
$\text{z}=\text{y}^{\text{n}+1}$
$\text{z}=\text{y}^{1-\text{n}}$