Download App

STD 12 - 7.1 inderfinite integral — JEE STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 ScienceJEESTD 12 - 7.1 inderfinite integral4 Marks
MCQ
$\int_{}^{} {\frac{{f'(x)}}{{{{[f(x)]}^2}}}} \;dx = $
  • ✓
    $ - {[f(x)]^{ - 1}} + c$
  • B
    $\log [f(x)] + c$
  • C
    ${e^{f(x)}} + c$
  • D
    None of these
✓

Answer

Correct option: A.
$ - {[f(x)]^{ - 1}} + c$
a
(a) Put $f(x) = t \Rightarrow f'(x)\,dx = dt,$ then
$\int_{}^{} {\frac{{f'(x)}}{{|f(x){|^2}}}\,dx} = \int_{}^{} {\frac{1}{{{t^2}}}\,dt} = - \frac{1}{t} + c = - \frac{1}{{f(x)}} + c.$

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

JEE STD 11 Science question papers→Gujarat Board STD 11 Science question papers→Gujarat Board question paper generator→

Similar questions

If $\vec a$ and $\vec b$ are non-zero vectors which are linearly dependent such that $\frac{{\left| {\vec a + \vec b} \right|}}{{\left| {\vec a - \vec b} \right|}}\, = \,2,\,\left| {\vec b} \right|\, > \,\left| {\vec a} \right|$ Then 
→
There are $n$ different objects $1, 2, 3,......n$ distributed at random in $n$ places marked $1, 2, 3, ......n$. The probability that at least three of the objects occupy places corresponding to their number is
→
If $\int {\frac{{dx}}{{{{\left( {{x^2} - 2x + 10} \right)}^2}}} = A\left( {{{\tan }^{ - 1}}\left( {\frac{{x - 1}}{3}} \right) + \frac{{f\left( x \right)}}{{{x^2} - 2x + 10}}} \right)}  + C$ Where $C$ is a constant of integration, then
→
Let $f(x)=\int_0^x g(t) \log _e\left(\frac{1-t}{1+t}\right) d t$, where $g$ is a continuous odd function. If $\int_{-\pi / 2}^{\pi / 2}\left(f(x)+\frac{x^2 \cos x}{1+e^x}\right) d x=\left(\frac{\pi}{\alpha}\right)^2-\alpha$, then $\alpha$ is equal to..............
→
If $x^{2}+9 y^{2}-4 x+3=0, x, y \in R$, then $x$ and $y$ respectively lie in the intervals:
→
If the set of all $a \in R$, for which the equation $2 x^2+$ $(a-5) x+15=3$ a has no real root, is the interval $(\alpha, \beta)$, and $X=\{x \in Z: \alpha < x < \beta\}$, then $\sum_{x \in X} x^2$ is equal to
→
Number of solutions of equation $sgn(sin x) = sin^2x + 2sinx + sgn(sin^2x)$ in $\left[ { - \frac{{5\pi }}{2},\frac{{7\pi }}{2}} \right]$  is

(where $sgn(.)$ denotes signum function) -

→
A ray of light coming from the point $P(1,2)$ gets reflected from the point $\mathrm{Q}$ on the $\mathrm{x}$-axis and then passes through the point $R(4,3)$. If the point $S(h$, $\mathrm{k})$ is such that $\mathrm{PQRS}$ is a parallelogram, then $\mathrm{hk}^2$ is equal to :
→
The mean of the data set comprising of $16$ observations is $16.$ If one of the observation valued $16$ is deleted and three new observations valued $3, 4$ and $5$ are added to the data, then the mean of the resultant data, is:
→
Let $\int x^3 \sin x d x=g(x)+C$, where $C$ is the constant of integration.
If $8\left(g\left(\frac{\pi}{2}\right)+g^{\prime}\left(\frac{\pi}{2}\right)\right)=\alpha \pi^3+\beta \pi^2+\gamma, \alpha, \beta, \gamma \in Z$,
Then $\alpha+\beta-\gamma$ equals :
→