_1^2 1 x^2 e^ - 1 x ,dx = - Vidyadip

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 STD 12 - 7.2 definite integral→STD 12 - 7.2 definite integral — all question types→Mathematics STD 12 Science question papers→CBSE Board STD 12 Science question papers→CBSE Board question paper generator→

Similar questions

$\int_{}^{} {\sqrt {{x^2} - 8x + 7} } \;dx = $

The minimum value of $Z = 3x + 5y$ subjected to constraints $\text{x}+3\text{y}\geq3,\text{x}+\text{y}\geq2,\text{x},\text{y}\geq0$ is :

$\left[ {\begin{array}{*{20}{c}}7&1&2\\9&2&1\end{array}} \right]\,\left[ \begin{array}{l}3\\4\\5\end{array} \right] + 2\left[ \begin{array}{l}4\\2\end{array} \right]$ is equal to

The function $\sin x - bx + c$ will be increasing in the interval $( - \infty ,\,\,\infty )$, if

The triangle formed by the points $(0, 7, 10), (-1, 6, 6), (-4, 9, 6)$ is

Let $m, n$ be two distinct integers chosen randomly from the set $\{0,1,2, \ldots, 99\}$. Then, the probability that $4^m+4^n+3$ is divisible by $5$ lies in the interval

Mark the correct alternative in the following question:
The probability that a person is not a swimmer is 0.3. The probability that out of 5 persons 4 are swimmers is:

If $\vec{\text{a}},\vec{\text{b}},\vec{\text{c}}$ are non-coplanar vectors, then $\frac{\vec{\text{a}}.\big(\vec{\text{b}}\times\vec{\text{c}}\big)}{\big(\vec{\text{c}}\times\vec{\text{a}}\big).\vec{\text{b}}}+\frac{\vec{\text{b}}.\big(\vec{\text{a}}\times\vec{\text{c}}\big)}{\vec{\text{c}}.\big(\vec{\text{a}}\times\vec{\text{b}}\big)}$ is equal to:

Let $[\lambda]$ be the greatest integer less than or equal to $\lambda$. The set of all values of $\lambda$ for which the system of linear equations $x+y+z=4,3 x+2 y+5 z=3$ $9 x+4 y+(28+[\lambda]) z=[\lambda]$ has a solution is:

Let $(\alpha, \beta, \gamma)$ be the point $(8,5,7)$ in the line $\frac{x-1}{2}=\frac{y+1}{3}=\frac{z-2}{5}$. Then $\alpha+\beta+\gamma$ is equal to