Download App

Integrals — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMathsIntegrals1 Mark
MCQ
Evaluate: $\int \frac{\sec ^2 x}{2+\tan x} d x$
  • A
    $\log |\tan x|+C$
  • B
    $\log |2-\tan x|+C$
  • ✓
    $\log |2+\tan x|+C$
  • D
    none of these
✓

Answer

Correct option: C.
$\log |2+\tan x|+C$
(c) : Let $I=\int \frac{\sec ^2 x}{2+\tan x} d x$
Put $2+\tan x=t \Rightarrow \sec ^2 x d x=d t$
$
\therefore \quad I=\int \frac{d t}{t}=\log |t|+C=\log |2+\tan 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 Integrals→Integrals — all question types→Maths STD 12 Science question papers→Gujarat Board STD 12 Science question papers→Gujarat Board question paper generator→

Similar questions

If $\hat{i}, \hat{j}, \hat{k}$ are unit vectors along three mutually perpendicular directions, then
→
Find the value of $x,$ if $\begin{bmatrix}1&-1\\3&-5\end{bmatrix}=\begin{bmatrix}\text{x}&\text{x}^2\\3&-5\end{bmatrix}$ is :
→
Differential equation

$\frac{{dy}}{{dx}} + \frac{1}{x}\sin 2y = {x^3}\,{\cos ^2}\,y$ represented by family of curves which is is givey by

→
$\int_{}^{} {\frac{{dx}}{{\sin x + \cos x}}} = $
→
Let $A = \{1, 2, 3\}$ and $B = \{(1, 2), (2, 3), (1, 3)\}$ be a relation on $A.$ Then, $R$ is:
→
$\big(\vec{\text{a}}+\vec{\text{b}}\big).\big(\vec{\text{b}}+\vec{\text{c}}\big)\times\big(\vec{\text{a}}+\vec{\text{b}}+\vec{\text{c}}\big)=$
→
If $\text{A}+\text{B}+\text{C}=\pi,$ then the value of $\begin{vmatrix}\sin(\text{A}+\text{B}+\text{C})&\sin(\text{A}+\text{C})&\cos\text{C}\\-\sin\text{B}&0&\tan\text{A}\\\cos(\text{A}+\text{B})&\tan(\text{B}+\text{C})&0\end{vmatrix}$ is equal to:
→
Choose the correct answer from the given four options. On using elementary row operation $R_1 \rightarrow R_1 – 3R_2$ in the following matrix equation $\begin{bmatrix}4&2\\3&3\end{bmatrix}=\begin{bmatrix}1&2\\0&3\end{bmatrix}\begin{bmatrix}2&0\\1&1\end{bmatrix},$ we have:
→
The function $f: R \rightarrow R$ defined by $f(x)=6^x+6^{|x|}$ is
→
$\int_0^\infty {\frac{{{x^3}\,dx}}{{{{({x^2} + 4)}^2}}} = } $
→