_ ^ 1 + x 2 ;dx = - Vidyadip

MCQ

$\int_{}^{} {\sqrt {1 + \sin \frac{x}{2}} \;dx = } $

A
$\frac{1}{4}\left( {\cos \frac{x}{4} - \sin \frac{x}{4}} \right) + c$
B
$4\left( {\cos \frac{x}{4} - \sin \frac{x}{4}} \right) + c$
✓
$4\left( {\sin \frac{x}{4} - \cos \frac{x}{4}} \right) + c$
D
$4\left( {\sin \frac{x}{4} + \cos \frac{x}{4}} \right) + c$

✓

Answer

Correct option: C.

$4\left( {\sin \frac{x}{4} - \cos \frac{x}{4}} \right) + c$

c
(c)$\int_{}^{} {\sqrt {1 + \sin \frac{x}{2}\,} } dx = \int_{}^{} {\sqrt {\left( {{{\sin }^2}\frac{x}{4} + {{\cos }^2}\frac{x}{4} + 2\sin \frac{x}{4}\cos \frac{x}{4}} \right)} \,dx} $
$ = \int_{}^{} {\left( {\sin \frac{x}{4} + \cos \frac{x}{4}} \right)\,dx = 4\left( {\sin \frac{x}{4} - \cos \frac{x}{4}} \right)} + 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

The value of $[a -b \,\,b -c\,\, c -a]$ , where $|a|\, = 1$,$|b|\,=5$ and $|c|\,=3$ is

If ${I_n} = \int_0^{\pi /4} {{{\tan }^n}\theta \,d\theta ,} $ then for any positive integer $n,$ the value of $n({I_{n - 1}} + {I_{n + 1}})$ is

$\int(3\text{x}^2-1)\text{dx:}$

x³ - x
x² - x
x³ - 1
None

Find the value of $\tan ^{-1}\left(2 \cos \left(2 \sin ^{-1} \frac{1}{2}\right)\right)$.

$\int_{}^{} {{e^{{{\cos }^2}x}}\sin 2x\;dx = } $

For, $\alpha, \beta, \gamma, \delta \in N$, if

$\int\left(\left(\frac{x}{e}\right)^{2 x}+\left(\frac{e}{x}\right)^{2 x}\right) \log _{ e } x d x=\frac{1}{\alpha}\left(\frac{ x }{ e }\right)^{\beta x}-\frac{1}{\gamma}\left(\frac{ e }{ x }\right)^{\delta x }+ C ,$

Where $e =\sum \limits_{ n =0}^{\infty} \frac{1}{ n !}$ and $C$ is constant of integration, then $\alpha+2 \beta+3 \gamma-4 \delta$ is equal to:

Let $\alpha, \beta, \gamma$ be the real roots of the equation, $x ^{3}+ ax ^{2}+ bx + c =0,( a , b , c \in R$ and $a , b \neq 0)$ If the system of equations (in, $u,v,w$) given by $\alpha u+\beta v+\gamma w=0, \beta u+\gamma v+\alpha w=0$ $\gamma u +\alpha v +\beta w =0$ has non-trivial solution, then the value of $\frac{a^{2}}{b}$ is

The integral $\int {\frac{{3{x^{13}}\, + \,\,2{x^{11}}}}{{{{(2{x^4}\, + \,3{x^2}\, + \,1)}^4}}}dx} $ is equal to (where $C$ is a constant of integration)

If a $3-$digit number is randomly chosen. What is the probability that either the number itself or some permutation of the number (which is a $3-$digit number) is divisible by $4$ and $5$ ?

A player $X$ has a biased coin whose probability of showing heads is $p$ and a player $Y$ has a fair coin . They start playing a game with their own coins and play alternately . The player who throws a head first is a winner. If $X$ starts the game, and the probability of winning the game by both the players is equal, then the value of $'p'$ is