_ ,0 ^ ,1 d dx [ ^ - 1 ( 2x 1 + x^2 ) ] ,dx is equal to - Vidyadip

MCQ

$\int_{\,0}^{\,1} {\frac{d}{{dx}}\left[ {{{\sin }^{ - 1}}\left( {\frac{{2x}}{{1 + {x^2}}}} \right)} \right]\,dx} $ is equal to

A
$0$
B
$\pi $
✓
$\pi /2$
D
$\pi /4$

✓

Answer

Correct option: C.

$\pi /2$

c
(c)$I = \left[ {{{\sin }^{ - 1}}\left( {\frac{{2x}}{{1 + {x^2}}}} \right)} \right]_0^1 = {\sin ^{ - 1}}(1) - {\sin ^{ - 1}}(0)$$ = \frac{\pi }{2}$.

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 7.2 definite integral→7.2 definite integral — all question types→Maths STD 12 Science question papers→Gujarat Board STD 12 Science question papers→Gujarat Board question paper generator→

Similar questions

If $A=\left[\begin{array}{lll}1 & 0 & 1 \\ 0 & 0 & 0 \\ 1 & 0 & 1\end{array}\right]$, then $A^2=$ ?

If $f$ be the greatest integer function and $g$ be the modulus function, then $(gof)\left( { - \frac{5}{3}} \right) - (fog)\left( { - \frac{5}{3}} \right) = $

Let $f$ be a function defined on $R$ (the set of all real numbers) such that $f^{\prime}(x)=2010(x-2009)(x-2010)^2$ $(x-2011)^3(x-2012)^4$, for all $x \in R$. If $g$ is a function defined on $R$ with values in the interval $(0, \infty)$ such that $f(x)=\ln (g(x))$, for all $x \in R$, then the number of points in $R$ at which $g$ has a local maximum is

Let $f:\left[ { - 2,3} \right] \to \left[ {0,\infty } \right)$ be a continuous function such that $f(1-x) = f(x)$ for all $x \in \left[ { - 2,3} \right]$ . If $R_1$ is the numerical value of the area of the region bounded by $y =f (x), x = -2, x = 3$ and the axis of $x$ and ${R_2} = \int\limits_{ - 2}^3 {x\,f\left( x \right)} dx$ , then

The area of the region (in the square unit) bounded by the curve ${x^2} = 4y,$ line $x = 2$ and $x-$ axis is

Let $\ln x$ denote the logarithm of $x$ with respect to the base $e$. Let $S \subset R$ be the set of all points where the function $\ln \left(x^2-1\right)$ is well-defined. Then, the number of functions $f: S \rightarrow R$ that are differentiable, satisfy $f^{\prime}(x)=\ln \left(x^2-1\right)$ for all $x \in S$ and $f(2)=0$, is

Let $l_{1}$ be the line in $xy$-plane with $x$ and $y$ intercepts $\frac{1}{8}$ and $\frac{1}{4 \sqrt{2}}$ respectively, and $l_{2}$ be the line in $zx$-plane with $x$ and $z$ intercepts $-\frac{1}{8}$ and $-\frac{1}{6 \sqrt{3}}$ respectively. If $d$ is the shortest distance between the line $l_{1}$ and $l_{2}$, then $d ^{-2}$ is equal to

Which of these are the direction cosines of the vector $-2 \hat{i}+\hat{j}-5 \hat{k}$ ?

If the points (p, 0), (0, q) and (1, 1) are collinear, then $\frac{1}{\text{p}}+\frac{1}{\text{q}}$ is equal to:

The probability that a student is not a swimmer is $\frac{1}{5}$. Then the probability that out of five students, four are swimmers is