( + ) 2 d = - Vidyadip

MCQ

$\int {\frac{{(\sin \theta + \cos \theta )}}{{\sqrt {\sin 2\theta } }}} d\theta = $

A
$\log \left| {\cos \theta - \sin \theta + \sqrt {\sin 2\theta } } \right|$
B
$\log \left| {\sin \theta - \cos \theta ) + \sqrt {\sin 2\theta } } \right|$
✓
${\sin ^{ - 1}}(\sin \theta - \cos \theta ) + c$
D
${\sin ^{ - 1}}(\sin \theta + \cos \theta ) + c$

✓

Answer

Correct option: C.

${\sin ^{ - 1}}(\sin \theta - \cos \theta ) + c$

c
(c) Let $I = \int {\frac{{\sin \theta + \cos \theta }}{{\sqrt {2\sin \theta \cos \theta } }}d\theta } $
$I = \int {\frac{{\sin \theta + \cos \theta }}{{\sqrt {1 - (1 - 2\sin \theta \cos \theta )} }}d\theta } $
$ = \int {\frac{{(\sin \theta + \cos \theta )d\theta }}{{\sqrt {1 - ({{\sin }^2}\theta + {{\cos }^2}\theta - 2\sin \theta \cos \theta )} }}} $
$ = \int {\frac{{\sin \theta + \cos \theta }}{{\sqrt {1 - {{(\sin \theta - \cos \theta )}^2}} }}d\theta } $
Let $(\sin \theta - \cos \theta ) = t$ ==> $(\cos \theta + \sin \theta )d\theta = dt$
$I = \int {\frac{{dt}}{{\sqrt {1 - {t^2}} }} = {{\sin }^{ - 1}}(t) + c} = {\sin ^{ - 1}}(\sin \theta - \cos \theta ) + c$.

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

The equation of motion of a car is $s = {t^2} - 2t$, where $t$ is measured in hours and $s$ in kilometers. When the distance travelled by the car is $15\,km$, the velocity of the car is ......... $km/h$.

$\int_{}^{} {{e^{x\log a}}.\;{e^x}\;dx} $is equal to

If the sum of the matrices $\begin{bmatrix}\text{x}\\\text{x}\\\text{y}\end{bmatrix},\begin{bmatrix}\text{x}\\\text{y}\\\text{z}\end{bmatrix}$ and $\begin{bmatrix}\text{z}\\0\\0\end{bmatrix}$ is the matrix $\begin{bmatrix}10\\5\\5\end{bmatrix},$ then what is the value of $y ?$

If $I _{1}=\int \limits_{0}^{1}\left(1- x ^{50}\right)^{100} dx$ and $I _{2}=\int \limits_{0}^{1}\left(1- x ^{50}\right)^{101} dx$ such that $I_{2}=\alpha I_{1}$ then $\alpha$ equals to

If $f(x)=\left\{\begin{array}{ll}x+a, & x \leq 0 \\ |x-4|, & x>0\end{array}\right.$ and $g(x)=\left\{\begin{array}{ll}x+1 & x<0 \\ (x-4)^{2}+b, & x \geq 0\end{array}\right.$ are continuous on $R$, then $(gof) (2)+( fog) (-2)$ is equal to.

If $x^y = e^{x-y}$ then $\frac{\text{dy}}{\text{dx}}$ is :

The maximum value of $Z = 4x + 3y$ subjected to the constraints $3x + 2y \geq 160, 5x + 2y \geq 200, x + 2y \geq 80, x, y \geq 0$ is :

The vectors $3\,i + j - 5\,k$ and $a\,i + b\,j - 15\,k$ are collinear, if

Choose the correct answer from the given four options. The vectors from origin to the points $A$ and $B$ are $\vec{\text{a}}=2\hat{\text{i}}-3\hat{\text{j}}+2\hat{\text{k}}$ and $\vec{\text{b}}=2\hat{\text{i}}+3\hat{\text{j}}+\hat{\text{k}},$ respectively, then the area of the triangle $\text{OAB}$ is :

Choose the correct answer from the given four options. If $A$ is matrix of order $m \times n$ and $B$ is a matrix such that $AB\ '$ and $B\ 'A$ are both defined, then order of matrix $B$ is: