1 + x 1 - x , ,dx = - Vidyadip

MCQ

$\int {\sqrt {\frac{{1 + x}}{{1 - x}}} \,\,dx = } $

A
$ - {\sin ^{ - 1}}x - \sqrt {1 - {x^2}} \, + c$
B
${\sin ^{ - 1}}x + \sqrt {1 - {x^2}} \, + c$
✓
${\sin ^{ - 1}}x - \sqrt {1 - {x^2}} \, + c$
D
$ - {\sin ^{ - 1}}x - \sqrt {{x^2} - 1} \, + c$

✓

Answer

Correct option: C.

${\sin ^{ - 1}}x - \sqrt {1 - {x^2}} \, + c$

c
(c)$I = \int {\sqrt {\frac{{1 + x}}{{1 - x}}} dx} $$ = \int {\frac{{1 + x}}{{\sqrt {1 - {x^2}} }}dx} $
$ = \int {\frac{{dx}}{{\sqrt {1 - {x^2}} }} + \int {\frac{x}{{\sqrt {1 - {x^2}} }}dx} } $$ = {\sin ^{ - 1}}x - \sqrt {1 - {x^2}} + 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

If $f(x) = a\sin (\log x)$, then ${x^2}f''(x) + xf'(x) = . . . $

The differential equation satisfied by $\text{ax}^{2}+\text{by}^{2}=1$ is :

Let $S=\{1,2,3,4,5,6\}$. Then the number of oneone functions $f: S \rightarrow P(S)$, where $P(S)$ denote the power set of $S$, such that $f(n) \subset f(m)$ where $n < m$ is $..................$

If f(x) = |3 − x| + (3 + x), where (x) denotes the least integer greater than or equal to x, then f(x) is:

$\int_0^{\pi /2} {\frac{{d\theta }}{{1 + \tan \theta }}} = $

For two events $A$ and $B$, if $P(A)=0.4, P(B)=0.8$ and $P(B / A)=0.6$, then $P(A \cup B)$ is

Let $\phi (x) = (x) + {2^{\log _x^3}} - {3^{\log _x^2}}$ then

Choose the correct answer from the given four options.
If $|\vec{{\text{a}}}|=10,|\vec{{\text{b}}}|=2$ and $\vec{{\text{a}}}\cdot\vec{{\text{b}}}=12,$ then value of $|\vec{{\text{a}}}\times\vec{\text{b}}|$ is:

If $y = {{\sqrt {a + x} - \sqrt {a - x} } \over {\sqrt {a + x} + \sqrt {a - x} }}$, then ${{dy} \over {dx}} = $

If $\begin{bmatrix}\cos\frac{2\pi}{7}&-\sin\frac{2\pi}{7}\\\sin\frac{2\pi}{7}&\cos\frac{2\pi}{7}\end{bmatrix}^\text{k}=\begin{bmatrix}1&0\\0&1\end{bmatrix},$ then the least positive integral value of k is: