Download App

7.1 inderfinite integral — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMaths7.1 inderfinite integral1 Mark
MCQ
$\int_{}^{} {\frac{{3{x^2}}}{{{x^6} + 1}}dx = } $
  • A
    $\log ({x^6} + 1) + c$
  • ✓
    ${\tan ^{ - 1}}({x^3}) + c$
  • C
    $3{\tan ^{ - 1}}({x^3}) + c$
  • D
    $3{\tan ^{ - 1}}\left( {\frac{{{x^3}}}{3}} \right) + c$
✓

Answer

Correct option: B.
${\tan ^{ - 1}}({x^3}) + c$
b
(b) Put ${x^3} = t \Rightarrow 3{x^2}dx = dt,$ therefore
$\int_{}^{} {\frac{{3{x^2}}}{{{x^6} + 1}}\,dx = \int_{}^{} {\frac{1}{{{t^2} + 1}}dt = {{\tan }^{ - 1}}(t) + c} }  = {\tan ^{ - 1}}({x^3}) + c$.

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 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

Evaluate: $\int\frac{1}{1+3\sin^2\text{x}+8\cos^2\text{x}}\text{dx}.$
  1. $\frac{1}{6}\tan^{-1}(2\tan\text{x})+\text{c}$
  2. $\tan^{-1}(2\tan\text{x})+\text{c}$
  3. $\frac{1}{6}\tan^{-1}(\frac{2\tan\text{x}}{3})+\text{c}$
  4. $\text{None of these}$
→
$\mathop {Limit}\limits_{n\,\, \to \,\,\infty } \, \frac{1}{n}\,\,\,\left[ {\,1\,\, + \,\,\sqrt {\frac{n}{{n\,\, + \,\,1}}} \,\,\, + \,\,\,\sqrt {\frac{n}{{n\,\, + \,\,2}}} \,\,\, + \,\,\,\sqrt {\frac{n}{{n\,\, + \,\,3}}} \,\,\, + \,\,\,.......\,\,\, + \,\,\,\sqrt {\frac{n}{{n\,\, + \,\,3\,\,(n\,\, - \,\,1)}}} \,} \right]$ has the value equal to
→
A homogeneous differential equation of the from $\frac{\text{dx}}{\text{dy}}=\text{h}\Big(\frac{\text{x}}{\text{y}}\Big)$ can be solved by making the substitution.

  1. y = vx

  2. v = yx

  3. x = vy

  4. x = v

→
If $a$  and $ b$ are mutually perpendicular vectors, then ${(a + b)^2} = $
→
For $0 < x < \frac{\pi }{2},\int\limits_{\frac{1}{2}}^{\frac{{\sqrt 3 }}{2}} {} $ ln $(e^{cos x})$. $d (sin\, x)$ is equal to :
→
In the set Z of all integers, which of the following relation R is not an equivalence relation?
  1. xRy : if $\text{x}\leq\text{y}$
  2. xRy : if x = y
  3. xRy : if x - y is an even integer
  4. xRy : if $\text{x}\equiv\text{y}\ (\text{mod 3})$
→
Evaluate: $\int(2\tan\text{x}-3\cot\text{x})^2\text{dx}.$
  1. $-4\tan\text{x}-\cot\text{x}-25\text{x}+\text{c}$
  2. $4\tan\text{x}-9\cot\text{x}-25\text{x}+\text{c}$
  3. $-4\tan\text{x}+9\cot\text{x}+25\text{x}+\text{c}$
  4. $4\tan\text{x}+9\cot\text{x}+25\text{x}+\text{c}$
→
Corner points of the feasible region determined by the system of linear constraints are $(0,3),(1,1)$ and $(3,0)$. Let $Z=p x+q y$, where $p, q>0$. Condition on $p$ and $q$ so that the minimum of $Z$ occurs at $(3,0)$ and $(1,1)$ is
→
$\int {\frac{{dx}}{{5 + 4\cos x}}} $ $= \lambda\, \tan^{-1}$ $\left( {m\tan \frac{x}{2}} \right)$ $+ C$ then :
→
If $A$ and $B$ are two events such that $P\,(A) = \frac{1}{3}$, $P\,(B) = \frac{1}{4}$ and $P\,(A \cap B) = \frac{1}{5},$ then $P\,\left( {\frac{{\overline B}}{{\overline A}}} \right) = $
→