Download App

7.1 inderfinite integral — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMaths7.1 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 7.1 inderfinite integral→7.1 inderfinite integral — all question types→Maths STD 12 Science question papers→Gujarat Board STD 12 Science question papers→Gujarat Board question paper generator→

Similar questions

In an LPP, if the objective function $Z=a x+b y$ has the same maximum value on two corner points of the feasible region, then the number of points at which $Z_{\max }$ occurs is
→
Let $\begin{vmatrix}\text{x}&2&\text{x}\\\text{x}^2&\text{x}&6\\\text{x}&\text{x}&6\end{vmatrix}=\text{ax}^4+\text{bx}^3+\text{cx}^2+\text{dx}+\text{e}.$ Then, the value of 5a + 4b + 3c + 2d + e is equal to:
  1. 0
  2. -16
  3. 16
  4. None of these.
→
What is the solution of the differential equation:
$\text{In}\Big(\frac{\text{dx}}{\text{dy}}\Big)-\text{a}=0?$ 
  1. y = xea + c
  2. x = yea + c
  3. y = In x + c
  4. x = In y + c
→
Five fair coins are tossed simultaneously. The probability of the events that atleast one head comes up is
→
Let $y=y(x)$ be the solution of the differential equation $\left(1-x^2\right) d y=\left[x y+\left(x^3+2\right) \sqrt{3\left(1-x^2\right)}\right] d x$ $-1 < x < 1, y(0)=0$. If $y\left(\frac{1}{2}\right)=\frac{\mathrm{m}}{\mathrm{n}}, \mathrm{m}$ and $\mathrm{n}$ are coprime numbers, then $\mathrm{m}+\mathrm{n}$ is equal to . . . . . . . . . .
→
For real $x$ with $-10 \leq x \leq 10$ define $f(x)=\int_{-10}^x 2^{[t]} d t$ where for a real number $r$ we denote by $[r]$ the largest integer less than or equal to $r$. The number of points of discontinuity of $f$ in the interval $(-10,10)$ is
→
Let $\mathrm{f}: R \rightarrow R$ and $\mathrm{g}: R \rightarrow R$ be defined as $f(x)=\left\{\begin{array}{lll}\log _e x & , & x>0 \\ e^{-x} & , & x \leq 0\end{array}\right.$ and $g(x)=\left\{\begin{array}{lll} x & , & x \geq 0 \\ e^{x} & , & x <  0\end{array}\right.$ Then $gof:R \to R$ is . . . . 
→
Let $\overrightarrow{\mathrm{a}}=\hat{\mathrm{i}}+5\, \hat{\mathrm{j}}+\alpha\, \hat{\mathrm{k}}, \overrightarrow{\mathrm{b}}=\hat{\mathrm{i}}+3 \,\hat{\mathrm{j}}+\beta\, \hat{\mathrm{k}}$ and $\overrightarrow{\mathrm{c}}=-\hat{\mathrm{i}}+2\, \hat{\mathrm{j}}-3 \,\hat{\mathrm{k}}$ be three vectors such that, $|\overrightarrow{\mathrm{b}} \times \overrightarrow{\mathrm{c}}|=5 \sqrt{3}$ and $\overrightarrow{\mathrm{a}}$ is perpendicular to $\overrightarrow{\mathrm{b}}$. Then the greatest amongst the values of $|\vec{a}|^{2}$ is .... .
→
For a steamer the consumption of petrol (per hour) varies as the cube of its speed (in km). If the speed of the current is steady at $C \,\,km/hr$ then the most economical speed of the steamer going against the current will be ........... $C$.
→
The area of the region enclosed by $y \leq 4 x^{2}, x^{2} \leq 9 y$ and $y \leq 4$, is equal tọ 
→