( ^ -1 x ) 1+x^2 d x= __________ , + C . - Vidyadip

MCQ

$\int \frac{\sin \left(\tan ^{-1} x\right)}{1+x^2} d x=$ __________ , + C .

A
$\cos \left(\tan ^{-1} x\right)$
B
$-\sin \left(\tan ^{-1} x\right)$
✓
$-\cos \left(\tan ^{-1} x\right)$
D
$\sin \left(\tan ^{-1} x\right)$

✓

Answer

Correct option: C.

$-\cos \left(\tan ^{-1} x\right)$

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 JUNE 2024→JUNE 2024 — all question types→Maths STD 12 Science question papers→Gujarat Board STD 12 Science question papers→Gujarat Board question paper generator→

Similar questions

The mapping f : N → N is given by f(n) = 1 + n², n ∈ N when N is the set of natural numbers is:

One-one and onto.
Onto but not one-one.
One-one but not onto.
Neither one-one nor onto.

The area of the region bounded by the curve $y=\cos x, x=0$ and $x=\frac{3 \pi}{2}$ is __________ .

Let $f : R \to R$ be defined by $f\left( x \right) = \frac{{\left| x \right| - 1}}{{\left| x \right| + 1}}$ then $f$ is

If $f(x) = $$\left\{ \begin{array}{l}\frac{{1 - (x)}}{{1 + x}},\,\,\,\,\,x \ne - 1\\\,\,1\,\,\,\,\,\,\,\,\,,\,\,\,\,\,x = - 1\end{array} \right.$, then the value of $f(|2k|)$ will be (where $[. ] $ shows the greatest integer function)

If $\vec{\text{a}}=2\hat{\text{i}}-3\hat{\text{j}}+5\hat{\text{k}},\vec{\text{b}}=3\hat{\text{i}}-4\hat{\text{j}}+5\hat{\text{k}}$ and $\vec{\text{c}}=5\hat{\text{i}}-3\hat{\text{j}}-2\hat{\text{k}},$ then the volume of the parallelopiped with contermious edges $\vec{\text{a}}+\vec{\text{b}},\vec{\text{b}}+\vec{\text{c}},\vec{\text{c}}+\vec{\text{a}}$ is:

2
1
-1
0

If $\left| {\,\begin{array}{*{20}{c}}{y + z}&x&y\\{z + x}&z&x\\{x + y}&y&z\end{array}\,} \right| = k(x + y + z){(x - z)^2}$, then $k = $

If $x = {{1 - {t^2}} \over {1 + {t^2}}}$ and $y = {{2at} \over {1 + {t^2}}}$, then ${{dy} \over {dx}} = $

The solution of the equation ${\sin ^{ - 1}}\left( {\frac{{dy}}{{dx}}} \right) = x + y$ is

$\left| {\,\begin{array}{*{20}{c}}{a - 1}&a&{bc}\\{b - 1}&b&{ca}\\{c - 1}&c&{ab}\end{array}\,} \right| = $

Let $R$ be the set of real numbers and $f: R \rightarrow R$ be defined by $f(x)=\frac{\{x\}}{1+[x]^2}$, where $[x]$ is the greatest integer less than or equal to $x$, and $\left\{x{\}}=x-[x]\right.$. Which of the following statements are true?

$I.$ The range of $f$ is a closed interval.

$II.$ $f$ is continuous on $R$.

$III.$ $f$ is one-one on $R$