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_{}^{} {\frac{x}{{1 + {x^4}}}\;dx = } $
  • A
    $\frac{1}{2}{\cot ^{ - 1}}{x^2} + c$
  • ✓
    $\frac{1}{2}{\tan ^{ - 1}}{x^2} + c$
  • C
    ${\cot ^{ - 1}}{x^2} + c$
  • D
    ${\tan ^{ - 1}}{x^2} + c$
✓

Answer

Correct option: B.
$\frac{1}{2}{\tan ^{ - 1}}{x^2} + c$
b
(b) Put $t = {x^2} \Rightarrow dt = 2x\,dx,$ therefore
$\int_{}^{} {\frac{x}{{1 + {x^4}}}\,dx = \frac{1}{2}\int_{}^{} {\frac{1}{{1 + {t^2}}}\,dt = \frac{1}{2}{{\tan }^{ - 1}}t + c = \frac{1}{2}{{\tan }^{ - 1}}{x^2} + c} } $.

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

A bag contains 5 brown and 4 white socks. A man pulls out two socks. The probability that these are of the sane colour is.
→
If $\quad A=\left[\begin{array}{cc}\cos \theta & \text { isin } \theta \\ \operatorname{isin} \theta & \cos \theta\end{array}\right], \left(\theta=\frac{\pi}{24}\right)$ and $A^{5}=\left[\begin{array}{ll}a & b \\ c & d\end{array}\right],$ where $i=\sqrt{-1},$ then which one of the following is not true?
→
The set of all $\alpha$, for which the vector $\vec{a}=\alpha t \hat{i}+6 \hat{j}-3 \hat{k} \quad$ and $\quad \vec{b}=t \hat{i}-2 \hat{j}-2 \alpha t \hat{k} \quad$ are inclined at an obtuse angle for all $t \in \mathbb{R}$ is :
→
The number of solutions of the equation
$\tan^{-1}2\text{x}+\tan^{-1}3\text{x}=\frac{\pi}{4}$ is:
→
Five persone entered the lift cabin on the ground floor of an $8$ floor house. Suppose that each of them independently and with equal probability can leave the cabin at any flor beginning with the first, then the probability of all $5$ persons leaving at different floors is,
→
$\int\limits_{ - \,1}^1 {\,\,\frac{{{x^3}\, + \,\,|x|\,\, + \,\,1}}{{{x^2}\, + \,\,2\,|x|\,\, + \,\,1}}}\,dx$ $= a\, ln\, 2 + b$ then :
→
If by dropping a stone in a quiet lake a wave moves in circle at a speed of  $3.5 \,cm/sec,$ then the rate of increase of the enclosed circular region when the radius of the circular wave is  $10$  $cm,$ is ......... $c{m^2}/sec$. $\left( {\pi = {{22} \over 7}} \right)$
→
The area of the triangle formed by the tangent and normal at the point $(1,\sqrt{3})$ on the circle $x^2 + y^2 = 4$ and the $x-$ axis is:
→
The given table shows the number of cars manufactured in four different colours on a particular day. Study it carefully and answer the question.
 
Number of cars manufactured
Colour
Vento
Creta
WagonR
Red
65
88
93
White
54
42
80
Black
66
52
88
Sliver
37
49
74
What was the total number of black cars manufactured?
→
If $(a, b, c)$ is the image of the point $(1,2,-3)$ in the line, $\frac{x+1}{2}=\frac{y-3}{-2}=\frac{z}{-1},$ then $a+b+c$ is equal to
→