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{{2x{{\tan }^{ - 1}}{x^2}}}{{1 + {x^4}}}} \;dx = $
  • A
    ${[{\tan ^{ - 1}}{x^2}]^2} + c$
  • ✓
    $\frac{1}{2}{[{\tan ^{ - 1}}{x^2}]^2} + c$
  • C
    $2{[{\tan ^{ - 1}}{x^2}]^2} + c$
  • D
    None of these
✓

Answer

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

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

Let $f: R \rightarrow R$ be defined $f(x)=a e^{2 x}+b e^x+c x$. If $f(0)=-1, f^{\prime}\left(\log _e 2\right)=21$ and $\int_0^{\log _e 4}(f(x)-c x) d x=\frac{39}{2}$, then the value of $|a+b+c|$ equals:
→
Choose the correct option from given four options:
$\int\limits^{\frac{\pi}{2}}_0\sqrt{1-\sin2\text{x}}\text{ dx}$ is equal to:
→
If the function $g\left( x \right) = \left\{ \begin{array}{l}
a{e^x},\,\,\,\,\,x \le 0\\
b\cos x + x,\,\,x > 0
\end{array} \right.\,\,\,\,\,\,$ is differentiable, then the value of $a^2 + b^2$ is
→
Let $f(x)=\max \{|x+1|,|x+2|, \ldots,|x+5|\}$. Then $\int_{-6}^{0} f(x) d x$ is equal to
→
Let $R = \{(a, a)\}$ be a relation on a set $A$. Then $R$ is
→
The vectors $\overrightarrow {AB} = 3i + 4k,$ and $\overrightarrow {AC} = 5i - 2j + 4k$ are the sides of a triangle $ABC$ . The length of the median through $A $ is
→
A line passes through $A(4,-6,-2)$ and $B(16,-2,4)$. The point $\mathrm{P}(\mathrm{a}, \mathrm{b}, \mathrm{c})$ where $\mathrm{a}, \mathrm{b}, \mathrm{c}$ are non-negative integers, on the line $\mathrm{AB}$ lies at a distance of 21 units, from the point $\mathrm{A}$. The distance between the points $\mathrm{P}(\mathrm{a}, \mathrm{b}, \mathrm{c})$ and $\mathrm{Q}(4,-12,3)$ is equal to...........
→
$\int_{}^{} {\frac{{dx}}{{{e^x} + {e^{ - x}}}} = } $
→
If $f: R \rightarrow R , f(x)=\sin x$ and $g: R \rightarrow R , g(x)=x^2$ then $(f o g)(x)$ is equal to :
→
The equation of the plane through point $(1, 2, -3)$ which is parallel to the plane $3x - 5y + 2z = 11$ is given by:
→