If 2^ 1 x x^2 dx=k 2^ 1 x +C, then k is equal to: - Vidyadip

MCQ

If $\int\frac{2^{\frac{1}{\text{x}}}}{\text{x}^2}\text{dx}=\text{k }2^{\frac{1}{\text{x}}}+\text{C},$ then $k$ is equal to:

✓
$-\frac{1}{\log_\text{e}2}$
B
$-\log_\text{e}2$
C
$-1$
D
$\frac{1}{2}$

✓

Answer

Correct option: A.

$-\frac{1}{\log_\text{e}2}$

$\text{k}=\int\frac{2^{\frac{1}{\text{x}}}}{\text{x}^2}\text{ dx}$
Put $\frac{1}{\text{x}}=\text{t}$
$\frac{-1}{\text{x}^2}\text{ dx}=\text{dt}$
$\frac{1}{\text{x}^2}\text{ dx}=-\text{dt}$
$\text{k}=\int2^{\text{t}}(-\text{dt})$
$\text{k}=\frac{-2^{\text{t}}}{\log_\text{e}2}+\text{C}$
$\text{k}=\frac{-2^{\frac{1}{\text{x}}}}{\log_\text{e}2}+\text{C}$
$\text{k}=\frac{-1}{\log_\text{e}2}$

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 Integrals→Integrals — all question types→Maths STD 12 Science question papers→Gujarat Board STD 12 Science question papers→Gujarat Board question paper generator→

Similar questions

Choose the correct answer in Exercise.
$\int\sqrt{1+\text{x}^2}\text{dx}$ is equal to

If $\frac{d y}{d x}+\frac{2^{x-y}\left(2^{y}-1\right)}{2^{x}-1}=0, x, y>0, y(1)=1$, then $y (2)$ is equal to

If $K \in R_0$ then det. $ |{adj (KI_n)}|$ is equal to

The mapping $f : N \rightarrow N$ is given by $f(n) = 1 + n^2, n \in N$ when $N$ is the set of natural numbers is:

$A = [a_{ij}]_{m \times n}$ is a square matrix, if:

If function $y = f(x)$ satisfy the differential equation $(x^3 + 1)dy = x(1 -3xy)dx$ and $f(0) = 0$ , then $\mathop {\lim }\limits_{x \to 0} \frac{{{x^2}}}{{f(x)}}$ is equal to

Let $a,b,c$ be positive real numbers. The following system of equations in $x, y$ and $ z $ $\frac{{{x^2}}}{{{a^2}}} + \frac{{{y^2}}}{{{b^2}}} - \frac{{{z^2}}}{{{c^2}}} = 1$, $\frac{{{x^2}}}{{{a^2}}} - \frac{{{y^2}}}{{{b^2}}} + \frac{{{z^2}}}{{{c^2}}} = 1, - \frac{{{x^2}}}{{{a^2}}} + \frac{{{y^2}}}{{{b^2}}} + \frac{{{z^2}}}{{{c^2}}} = 1$ has

Two matrices A and B are added if:

Area lying in the first quadrant and bounded by the circle $x^{2}+y^{2}=4$ and the lines $x=0$ and $x=2$ is

If $A=\left[a_{i j}\right]$ is a scalar matrix of order $n \times n$ such that $a_{i j}=k$ for all $i$, then trace of $A$ is equal to