Download App

7.2 definite integral — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMaths7.2 definite integral1 Mark
MCQ
If $f(t) = \int_{\, - t}^{\,t} {\frac{{dx}}{{1 + {x^2}}},} $ then $f'(1)$ is
  • A
    $Zero$
  • B
    $2/3$
  • C
    $ - \,1$
  • ✓
    $1$
✓

Answer

Correct option: D.
$1$
d
(d) Given $f(t) = \int_{ - t}^t {\frac{{dx}}{{1 + {x^2}}}} $

$ = [{\tan ^{ - 1}}x]_{ - t}^t$

$ = 2{\tan ^{ - 1}}t$

Differentiating with respect to $t$,

$f'(t) = \frac{2}{{1 + {t^2}}}$

==> $f'(1) = \frac{2}{2} = 1$.

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

Let $f(x)=(x+3)^2(x-2)^3, x \in[-4,4]$. If $M$ and $m$ are the maximum and minimum values of $f$, respectively in $[-4,4]$, then the value of $M-m$ is :
→
$\int_0^{\pi /4} {} (\cos x - \sin x)dx + \int_{\pi /4}^{5\pi /4} {} (\sin x - \cos x)dx$ $ + \int_{2\pi }^{\pi /4} {} (\cos x - \sin x)\,dx$ is equal to
→
$\mathop {Lim}\limits_{\lambda  \to 0} \,\,{\left( {\int\limits_0^1 {{{(1 + x)}^\lambda }dx} } \right)^{\frac{1}{\lambda }}}$ is equal to
→
Choose the correct answer from the given four options.
Let f : R → R be defined by $\text{f}(\text{x})=\begin{cases}2\text{x}:\text{x}>3\\\text{x}^2:1<\text{x}\leq3\\3\text{x}:\text{x}\leq1\end{cases}$ Then f(-1) + f(2) + f(4) is:
  1. 9
  2. 14
  3. 5
  4. none of these.
→
If A is a matrix of order m × n and B is a matrix such that ABT and BT A are both defined, then the order of matrix B is:
  1. m × m
  2. n × n
  3. n × m
  4. m × n
→
The equation of normal to the curve 3x2 - y2 = 8 which is parallel to the line x + 3y = 8 is:
  1. 3x - y = 8
  2. 3x + y + 8 = 0
  3. $\text{x + 3y} \underline{+} 8 = 0$
  4. x + 3y = 0
→
A vector of length $3$  perpendicular to each of the vectors $3\,i + j - 4\,k$ and $6\,i + 5\,j - 2\,k$ is
→
Choose the correct answer from the given four options.
If $\text{P}(\text{A})=\frac{4}{5},$ and $\text{P}(\text{A}\cap\text{B})=\frac{7}{10},$ then $\text{P}\Big(\frac{\text{B}}{\text{A}}\Big)$ is equal to:
  1. $\frac{1}{10}$
  2. $\frac{1}{8}$
  3. $\frac{7}{8}$
  4. $\frac{17}{20}$
→
$\int {\frac{{{e^{\sqrt x }}}}{{\sqrt x }}\,\,\left( {x + \sqrt x } \right)\,\,dx\,} $
→
If $\text{A}=\displaystyle \begin{vmatrix} 1 \\ 3 \end{vmatrix}\text{B}=\displaystyle \begin{vmatrix} -1 \\ 4 \end{vmatrix}$  then $ 2\text{A}+\text{B} =$
  1. $\displaystyle \begin{vmatrix} 10 \\ 9 \end{vmatrix}$
  2. $\displaystyle \begin{vmatrix} 10 \\ 1 \end{vmatrix}$
  3. $\displaystyle \begin{vmatrix} 1 \\ 10 \end{vmatrix}$
  4. $\displaystyle \begin{vmatrix} 1 \\ 9 \end{vmatrix}$
→