Download App

STD 12 - 7.1 inderfinite integral — Mathematics STD 12 Science — Question

CBSE BoardEnglish MediumSTD 12 ScienceMathematicsSTD 12 - 7.1 inderfinite integral1 Mark
MCQ
$\int_{}^{} {{{\tan }^{ - 1}}x\,dx = } $
  • A
    $x{\tan ^{ - 1}}x + \frac{1}{2}\log (1 + {x^2})$
  • ✓
    $x{\tan ^{ - 1}}x - \frac{1}{2}\log (1 + {x^2})$
  • C
    $(x - 1){\tan ^{ - 1}}x$
  • D
    $x{\tan ^{ - 1}}x - \log (1 + {x^2})$
✓

Answer

Correct option: B.
$x{\tan ^{ - 1}}x - \frac{1}{2}\log (1 + {x^2})$
b
(b)$\int_{}^{} {{{\tan }^{ - 1}}x\,dx} = x{\tan ^{ - 1}}x - \int_{}^{} {\frac{x}{{1 + {x^2}}}\,dx + c} $
$ = x{\tan ^{ - 1}}x - \frac{1}{2}\log (1 + {x^2}) + c.$
Note : Students should remember this question as a formula.

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

The corner points of the bounded feasible region determined by a system of linear constraints are $(0,3),(1,1)$ and $(3,0)$. Let $Z=p x+q y$, where $p, q>0$,. The condition on $p$ and $q$ so that the minimum of $Z$ occurs at $(3,0)$ and $(1,1)$ is
→
If $A$ and $B$ are symmetric matrices of the same order, then:
→
The area bounded by the curve $y^2=x,$ line $y=4$ and $y-$axis is:
→
Let the mean and the standard deviation of the probability distribution

$X$ $\alpha$ $1$ $0$ $-3$
$P(X)$ $\frac{1}{3}$ $K$ $\frac{1}{6}$ $\frac{1}{4}$

be $\mu$ and $\sigma$, respectively. If $\sigma-\mu=2$, then $\sigma+\mu$ is equal to....................

→
The number of points of discontinuity of $f(x)$ where $f(x) = \left| {\left| {\left| {x + \left[ x \right]} \right| - 3\left[ x \right]} \right| - 5\left[ x \right]} \right|$ on $[-2 , 2]$ is (where $[ · ]$ denotes greatest integer function)
→
The area of the region bounded by the curve $x^2 = 4y$ and the straight line $x = 4y - 2$ is:
→
If $AB = A$ and $BA = B$, then
→
If $\triangle_1=\begin{vmatrix}1&1&1\\\text{a}&\text{b}&\text{c}\\\text{a}^2&\text{b}^2&\text{c}^2\end{vmatrix},\triangle_2=\begin{vmatrix}1&\text{bc}&\text{a}\\1&\text{ca}&\text{b}\\1&\text{ab}&\text{c}\end{vmatrix},$ then:
→
Choose the correct answer from the given four options:
The area of the region bounded by the y-axis, $\text{y}=\cos\text{x}$ and $\text{y}=\sin\text{x},0\leq\text{x}\leq\frac{\pi}{2}$ is:
→
If $\text{A}=\begin{bmatrix} 3 & 4 \\ 2 & 4 \end{bmatrix},\text{B}=\begin{bmatrix} -2 & -2 \\ 0 & -1 \end{bmatrix}$ then $(A + B)^{-1} =$
→