Download App

7.2 definite integral — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMaths7.2 definite integral1 Mark
MCQ
$\int_{\,0}^{\,1} {\,{{\tan }^{ - 1}}\left( {\frac{1}{{{x^2} - x + 1}}} \right)\,dx} $ is
  • A
    $ln\ 2$
  • B
    $ - \ln 2$
  • C
    $\frac{\pi }{2} + \ln 2$
  • ✓
    $\frac{\pi }{2} - \ln 2$
✓

Answer

Correct option: D.
$\frac{\pi }{2} - \ln 2$
d
(d) $\int_0^1 {{{\tan }^{ - 1}}\left( {\frac{1}{{{x^2} - x + 1}}} \right)\,dx} $

$= \int_0^1 {{{\tan }^{ - 1}}x\,dx - } \int_0^1 {{{\tan }^{ - 1}}(x - 1)} \,dx$

$ = 2\int_{\,0}^{\,1} {{{\tan }^{ - 1}}x\,dx} $

$= 2\,[{\tan ^{ - 1}}x - \frac{1}{2}\log (1 + {x^2})]_0^1 $

$= \frac{\pi }{2} - \log 2.$

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

The value of the integral $\int_{0}^{\frac{\pi}{2}} 60 \frac{\sin (6 x)}{\sin x} d x$ is equal to.
→
Consider a binary operation ∗ on N defined as a ∗ b = a3 + b3.
  1. ∗ is both associative and commutative.
  2. ∗ is commutative but not associative.
  3. ∗ is neither commutative nor associative.
  4. ∗ is associative but not commutative.
→
${d \over {dx}}[\cos {(1 - {x^2})^2}]$=
→
A point P lies on the line segment joining the points (-1, 3, 2) and (5, 0, 6). If x-coordinate of P is 2, then its z-coordinate is:
  1. $-1$
  2. $4$
  3. $\frac{3}{2}$
  4. $8$
→
$\int\frac{(1+\text{log x})^2}{1+\text{x}^2}\text{dx}=$
  1. $\frac{1}{3}(1+\text{log})^3+\text{c}$
  2. $\frac{1}{2}(1+\text{log})^2+\text{c}$
  3. $\log(\text{log }1+\text{x})+2$
  4. $\text{None of these}$
→
$\int\limits_0^{\frac{\pi }{2}} {\,\,\frac{{dx}}{{1\,\, + \,\,{a^2}{{\sin }^2}x}}} $ has the value :
→
Choose the correct answer from the given four options.

Let f : R → R be defined by f(x) = 3x2 – 5 and g : R → R by $\text{g}(\text{x})=\frac{\text{x}}{\text{x}^2+1}.$ Then gof is:

  1. $\frac{3\text{x}^2-5}{9\text{x}^4-30\text{x}^2+26}$

  2. $\frac{3\text{x}^2-5}{9\text{x}^4-6\text{x}^2+26}$

  3. $\frac{3\text{x}^2}{\text{x}^4+2\text{x}^2-4}$

  4. $\frac{3\text{x}^2}{9\text{x}^4+30\text{x}^2-2}$

→
Let $f(x)=\left|\begin{array}{ccc}a & -1 & 0 \\ a x & a & -1 \\ a x^{2} & a x & a\end{array}\right|, a \in R$. Then the sum of which the squares of all the values of a for $2 f^{\prime}(10)-f^{\prime}(5)+100=0$ is
→
Given $f (x) =4\,\, - \,\,{\left( {\frac{1}{2}\, - \,x} \right)^{2/3}}\,$ $g (x) = \left\{ \begin{array}{l}\frac{{\tan \,\,[x]}}{x}\,\,\,\,,\,\,x \ne \,0\\1\,\,\,\,\,\,\,\,\,\,\,\,\,,\,\,\,x\, = \,0\end{array} \right.$

$h (x) = \{x\}$   $k (x) = {5^{{{\log }_2}(x\, + \,3)}}$then in $[0, 1]$ Lagranges Mean Value Theorem is $NOT$ applicable to

→
If ${y^2} = a{x^2} + bx + c$, then ${y^3}{{{d^2}y} \over {d{x^2}}}$ is
→