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{{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

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

Two persons $A$ and $B$ take turns in throwing a pair of dice.The first person to throw $9$ from both dice will be awarded the prize. If $A$ throws first, then the probability that $B$ wins the game is.
→
A value of $\theta  \in  (0, \pi /3)$, for which $\left| {\begin{array}{*{20}{c}}
  {1 + {{\cos }^2}\,\theta }&{{{\sin }^2}\,\theta }&{4\,\cos \,6\theta } \\ 
  {{{\cos }^2}\,\theta }&{1 + {{\sin }^2}\,\theta }&{4\,\cos \,6\theta } \\ 
  {{{\cos }^2}\,\theta }&{{{\sin }^2}\,\theta }&{1 + 4\,\cos \,6\theta } 
\end{array}} \right| = 0$, is
→
Let the area of the region $\{(x, y): x-2 y+4 \geq 0$, $\left.x+2 y^2 \geq 0, x+4 y^2 \leq 8, y \geq 0\right\}$ be $\frac{m}{n}$, where $m$ and $\mathrm{n}$ are coprime numbers. Then $\mathrm{m}+\mathrm{n}$ is equal to
→
Choose the correct answer from the given four options : The area of the region bounded by the curve $\text{y}=\sqrt{16-\text{x}^2}$ and $x-$ axis is :
→
Let $f(x) = |x|$ and $g(x) = |x^3|,$ then:
→
The number of all possible matrices of order 3 × 3 with each entry 0 or 1 is:
→
Choose the correct answer from given four options in each of the Exercise:
The value of $\begin{vmatrix}\text{a}-\text{b}&\text{b}+\text{c}&\text{a}\\\text{b}-\text{a}&\text{c}+\text{a}&\text{b}\\\text{c}-\text{a}&\text{a}+\text{b}&\text{c}\end{vmatrix}$ is:
→
A spherical balloon is expanding. If at any instant rate of increase of its volume is $16\, times $ of rate of increase of its radius, then its radius at that instant, is
→
Function $f(x) = \frac{{1 - \cos 4x}}{{8{x^2}}},$ where $x \ne 0$and $f(x) = k$ where $x = 0$ is a continous function at $x = 0$ then the value of $k$ will be $k = $ ........
→
If $I = \int {\frac{{{{\sin }^2}\,x\, - \,1}}{{2x{{\sin }^2}x + \,\sin 2x}}dx} $ , then. . . . .         $(sinx \neq  0)$ 

(where $c$ is positive constant of integration)

→