_ ^ ^2 x ;dx ^2 x + 4 = - Vidyadip

MCQ

$\int_{}^{} {\frac{{{{\sec }^2}x\;dx}}{{\sqrt {{{\tan }^2}x + 4} }} = } $

✓
$\log \left[ {\tan x + \sqrt {{{\tan }^2}x + 4} } \right] + c$
B
$\frac{1}{2}\log \left[ {\tan x + \sqrt {{{\tan }^2}x + 4} } \right] + c$
C
$\log \left[ {\frac{1}{2}\tan x + \frac{1}{2}\sqrt {{{\tan }^2}x + 4} } \right] + c$
D
None of these

✓

Answer

Correct option: A.

$\log \left[ {\tan x + \sqrt {{{\tan }^2}x + 4} } \right] + c$

a
(a) Put $t = \tan x \Rightarrow dt = {\sec ^2}x\,dx,$ then
$\int_{}^{} {\frac{{{{\sec }^2}x\,dx}}{{\sqrt {{{\tan }^2}x + 4} }}} = \int_{}^{} {\frac{1}{{\sqrt {{t^2} + {2^2}} }}} \,dt$
$ = \log [\tan x + \sqrt {{{\tan }^2}x + 4} ] + 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

If $\int_2^e {\left[ {\frac{1}{{\log x}} - \frac{1}{{{{(\log x)}^2}}}} \right]} \,dx = \alpha + \frac{\beta }{{\log 2}},$ then

Area of the region bounded by the curve $y=x|x|$, X -axis and lines $x=0$ and $x=1$ is ___________ sq. units.

Let $\vec{x}, \vec{y}$ and $\vec{z}$ be three vectors each of magnitude $\sqrt{2}$ and the angle between each pair of them is $\frac{\pi}{3}$. If $\vec{a}$ is a nonzero vector perpendicular to $\vec{x}$ and $\vec{y} \times \vec{z}$ and $\vec{b}$ is a nonzero vector perpendicular to $\vec{y}$ and $\overrightarrow{ z } \times \overrightarrow{ x }$, then

$(A)$ $\vec{b}=(\vec{b} \cdot \vec{z})(\vec{z}-\vec{x})$

$(B)$ $\vec{a}=(\vec{a} \cdot \vec{y})(\vec{y}-\vec{z})$

$(C)$ $\vec{a} \cdot \vec{b}=-(\vec{a} \cdot \vec{y})(\vec{b} \cdot \vec{z})$

$(D)$ $\vec{a}=(\vec{a} \cdot \vec{y})(\vec{z}-\vec{y})$

$\int\limits_0^{\frac{\pi }{2}} {\,\,\sqrt {\sin \,2\theta } } \sin\, \theta \,d\theta$ is equal to :

If the position vectors of the vertices $A, B$ and $C$ of a $ \Delta ABC$ are respectively $4\hat i + 7\hat j + 8\hat k\,,\,2\hat i + 3\hat j + 4\hat k$ and $2\hat i + 5\hat j + 7\hat k$ then the position vector of the point, where the bisector of $\angle A$ meets $BC$ is

The area of the region bounded by parabola $y^2=x$ and the straight line $2 y=x$ is

$\left| {\,\begin{array}{*{20}{c}}1&{1 + ac}&{1 + bc}\\1&{1 + ad}&{1 + bd}\\1&{1 + ae}&{1 + be}\end{array}\,} \right| = $

$z=30 x-30 y+1800$ is a objective function. The corner points of the feasible region are $(15,0),(15,15),(10,20),(0,20)$ and $(0,15) $. $z$ has the minimum value at $\ldots \ldots \ldots .$ point.

The position vectors of two points $ A$ and $B$ are $i + j - k$ and $2i - j + k$ respectively. Then $|\overrightarrow {AB} |\,\, = $

Let $H$ be the set of all houses in a village where each house is faced in one of the directions, East, West, North, South. Let $R = \{ (x,y)|(x,y) \in H \times H$ and $x, y$ are faced in same direction $\}$ . Then the relation $' R '$ is