Download App

7.2 definite integral — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMaths7.2 definite integral1 Mark
MCQ
$\int_1^2 {\frac{1}{{{x^2}}}{e^{\frac{{ - 1}}{x}}}\,dx = } $
  • A
    $\sqrt e + 1$
  • B
    $\sqrt e - 1$
  • C
    $\frac{{\sqrt e + 1}}{e}$
  • ✓
    $\frac{{\sqrt e - 1}}{e}$
✓

Answer

Correct option: D.
$\frac{{\sqrt e - 1}}{e}$
d
(d) Put $t = - \frac{1}{x} \Rightarrow dt = \frac{1}{{{x^2}}}dx$,

then it reduces to 

$\int_{ - 1}^{ - 1/2} {{e^t}dt = [{e^t}]_{ - 1}^{ - 1/2} = {e^{ - 1/2}} - {e^{ - 1}}} = \frac{{\sqrt e - 1}}{e}$.

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 7.2 definite integral→7.2 definite integral — all question types→Maths STD 12 Science question papers→Gujarat Board STD 12 Science question papers→Gujarat Board question paper generator→

Similar questions

The __________ is the method available for solving an L.P.P
  1. Graphical method
  2. Least cost method
  3. MODI method
  4. Hungarian method
→
The sum of two non-zero numbers is $4$ . The minimum value of the sum of their reciprocals is
→
The solution of the differential equation $({x^2} + {y^2})dx = 2xydy$ is
→
If the value of the integral $\int_{-\frac{\pi}{2}}^{\frac{\pi}{2}}\left(\frac{x^2 \cos x}{1+\pi^x}+\frac{1+\sin ^2 x}{1+e^{\sin x^{323}}}\right) d x=\frac{\pi}{4}(\pi+a)-2$, then the value of $a$ is
→
If $A = \left( {\begin{array}{*{20}{c}}
{\alpha  - 1}\\
0\\
0
\end{array}} \right),\,\,\,B = \left( {\begin{array}{*{20}{c}}
{\alpha  + 1}\\
0\\
0
\end{array}} \right)$ be two matrices, then $AB^T$ is a non-zero matrix for $\left| \alpha  \right|$ not equal to
→
The d.rs of the lines x = ay + b, z = cy + d are:
  1. 1, a, c
  2. a, 1, c
  3. b, 1, c
  4. c, a, 1
→
A coin is tossed three times. If events A and B are defined as A = Two heads come, B = Last should be head, Then, A and B are
  1. Independent.
  2. Dependent.
  3. Both.
  4. Mutually exclusive.
→
The values of $\alpha$, for which $\left|\begin{array}{ccc}1 & \frac{3}{2} & \alpha+\frac{3}{2} \\ 1 & \frac{1}{3} & \alpha+\frac{1}{3} \\ 2 \alpha+3 & 3 \alpha+1 & 0\end{array}\right|=0$, lie in the interval
→
$[i k j]+[k j i]+[j k i]$
→
If $\text{y}^2=\text{ax}^2+\text{bx}+\text{c},$ then $\text{y}^3\frac{\text{d}^2\text{y}}{\text{dx}^2}$ is:
  1. a constant
  2. a function of x only
  3. a function of y only
  4. a function of x and only
→