^2 , , ( , + , )^2 , ,d - Vidyadip

MCQ

$\int {{{\sec }^2}\theta } \,\,{(\sec \theta \, + \,\tan \theta )^2}\,\,d\theta $

A
$\frac{{(\sec \theta \, + \,\tan \theta )}}{2}\,[2\, + \,\tan \theta \,(\sec \theta \, + \,\tan \theta )]\,\, + \,\,C$
B
$\frac{{(\sec \theta \, + \,\tan \theta )}}{3}\,[2\, + \,4\tan \theta \,(\sec \theta \, + \,\tan \theta )]\,\, + \,\,C$
✓
$\frac{{(\sec \theta \, + \,\tan \theta )}}{3}\,[2\, + \,\tan \theta \,(\sec \theta \, + \,\tan \theta )]\,\, + \,\,C$
D
$\frac{{3\,(\sec \theta \, + \,\tan \theta )}}{2}\,[2\, + \,\tan \theta \,(\sec \theta \, + \,\tan \theta )]\,\, + \,\,C$

✓

Answer

Correct option: C.

$\frac{{(\sec \theta \, + \,\tan \theta )}}{3}\,[2\, + \,\tan \theta \,(\sec \theta \, + \,\tan \theta )]\,\, + \,\,C$

c
put $\sec\, \theta + \tan \, \theta = t$

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

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:

If $\text{A}=\begin{bmatrix} 2 & -1 \\ 3 & -2 \end{bmatrix},$ then $A^n =$

Let $f$ be a composite function of $x$ defined by $f\left( u \right) = \frac{1}{{{u^2} + u - 2}}\,,\,u\left( x \right) = \frac{1}{{x - 1}}$ . Then the number of points $x$ where $f$ is discontinuous is

Let $A$ be a square matrix such that ${a_{ij}} \in \left\{ { - 1,0,1} \right\}\forall\,\, i,j$ and it has only one non-zero entry in each row as well as in each column, then

Let $f(x)\, = \left\{ {\begin{array}{*{20}{c}}{x + 1,}&{{\rm{when}}}&{x < 2}\\{2x - 1,}&{{\rm{when}}}&{x \ge 2}\end{array}} \right.\,,\,$ then $f'(2) = $

Function f(x) = |x| - |x - 1| is monotonically increasing when:

Let $f(x)=\frac{\sin (x-a)+\sin (x+a)}{\cos (x-a)-\cos (x+a)}$, then

If $A\,(1\,,\,\,2,\,\, - 1)$ and $B( - 1,\,\,0,\,\,1)$ are given, then the co-ordinates of $P $ which divides $AB$ externally in the ratio $1:2$, are

The function $f(x) = sgnx\,\cdot \,sinx$ is

Integrating factor of the differential equation, $(1-\text{x}^2)\frac{\text{dy}}{\text{dx}}-\text{xy}=1$ is: