^ - 1 x - ^ - 1 x ^ - 1 x + ^ - 1 x dx = - Vidyadip

MCQ

$\int {\frac{{{{\sin }^{ - 1}}x - {{\cos }^{ - 1}}x}}{{{{\sin }^{ - 1}}x + {{\cos }^{ - 1}}x}}} dx = $

✓
$\frac{4}{\pi }\left( {x{{\sin }^{ - 1}}x + \sqrt {1 - {x^2}} } \right) - x + c$
B
$\log |{\sin ^{ - 1}}x + {\cos ^{ - 1}}x| + c$
C
$\frac{4}{\pi }\left( {x{{\sin }^{ - 1}}x + \sqrt {1 - {x^2}} } \right) + c$
D
None of these

✓

Answer

Correct option: A.

$\frac{4}{\pi }\left( {x{{\sin }^{ - 1}}x + \sqrt {1 - {x^2}} } \right) - x + c$

a
$\int \frac{\sin ^{-1} x-\left(\pi / 2-\sin ^{-1} x\right)}{\pi / 2} d x$

$\left.\frac{2}{\pi} \int 2 \sin ^{-1} x-\pi / 2\right) d x$

$\frac{4}{\pi} \int \sin ^{-1} x d x-\int d x$

$\frac{4}{\pi}\left[\int x \sin ^{-1} x-\int \frac{x d x}{\sqrt{1-x^{2}}}\right]-x+c$

$\frac{4}{\pi}\left[x \sin ^{-1} x+\sqrt{1-x^{2}}\right]-x+c$

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 $\text{A}=\begin{bmatrix} 3 & 4 \\ 2 & 4 \end{bmatrix},\text{B}=\begin{bmatrix} -2 & -2 \\ 0 & -1 \end{bmatrix}$ then $(A + B)^{-1} =$

The value of $\int_{-\pi}^\pi \frac{2 y(1+\sin y)}{1+\cos ^2 y} d y$ is :

Let $\overrightarrow{\mathrm{OA}}=2 \overrightarrow{\mathrm{a}}, \overrightarrow{\mathrm{OB}}=6 \overrightarrow{\mathrm{a}}+5 \overrightarrow{\mathrm{b}}$ and $\overrightarrow{\mathrm{OC}}=3 \overrightarrow{\mathrm{b}}$, where $O$ is the origin. If the area of the parallelogram with adjacent sides $\overrightarrow{\mathrm{OA}}$ and $\overrightarrow{\mathrm{OC}}$ is $15$ sq. units, then the area (in sq. units) of the quadrilateral $\mathrm{OABC}$ is equal to :

Let $A=\left[\begin{array}{cc}1 & \frac{1}{51} \\ 0 & 1\end{array}\right]$. If $B=\left[\begin{array}{cc}1 & 2 \\ -1 & -1\end{array}\right] A \left[\begin{array}{cc}-1 & -2 \\ 1 & 1\end{array}\right]$ then the sum of all the elements of the matrix $\sum \limits_{n=1}^{50} B^n$ is equal to

The differential equation which respresents the famliy of curves $\text{y}=\text{e}^{\text{Cx}}$ is :

If ${D_p} = \left| {\,\begin{array}{*{20}{c}}p&{15}&8\\{{p^2}}&{35}&9\\{{p^3}}&{25}&{10}\end{array}\,} \right|$, then ${D_1} + {D_2} + {D_3} + {D_4} + {D_5} = $

If the function $\text{f}(\text{x})=2\tan\text{x}+(2\text{a}+1)\log_\text{e}|\sec\text{x}|+(\text{a}-2)\text{x}$ is increasing on R, then:

Let the function $f$ be defined by $f(x) = \frac{{2x + 1}}{{1 - 3x}}$, then ${f^{ - 1}}(x)$ is

Let a function $g:[0,4] \rightarrow R$ be defined as

$g ( x )=\left\{\begin{array}{ll}\max _{0 \leq t \leq x }\left\{ t ^{3}-6 t ^{2}+9 t -3\right\} & , 0 \leq x \leq 3 \\ 4- x & , 3 < x \leq 4\end{array}\right.$ then the number of points in the interval $(0,4)$ where $g(x)$ is NOT differentiable, is $.....$

Let $f(x) =\left\{ \begin{gathered}
x{e^{3x}},\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,x \leqslant 0 \hfill \\
- {x^3}\, + \,3{x^3}\, + \,x,\,\,x > 0 \hfill \\
\end{gathered} \right.,$ then complete values of $x$ for which $f'(x)$ is increasing function is