If _ ^ f(x) ,dx = x e^ - |x| + f(x), then f(x) is - Vidyadip

MCQ

If $\int_{}^{} {f(x)\,dx} = x{e^{ - \log |x|}} + f(x),$ then $f(x)$ is

A
$1$
B
$0$
✓
$c{e^x}$
D
$\log x$

✓

Answer

Correct option: C.

$c{e^x}$

c
(c) $\int_{}^{} {f(x)dx = x{e^{\log \left| {\frac{1}{x}} \right|}} + f(x) \Rightarrow \int_{}^{} {f(x)dx = \frac{x}{{|x|}} + f(x)} } $

On differentiating both sides , we get $f(x) = 0 + f'(x)$

We know $\frac{d}{{dx}}({e^x}) = {e^x},\,\,$

$\therefore \,\,f(x) = c{e^x}$.

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 ${z^2} + z + 1 = 0$, where $z$ is complex number,then the value of ${\left( {z + \ \frac{1}{z}} \right)^2} + {\left( {{z^2} + \frac{1}{{{z^2}}}} \right)^2} + {\left( {{z^3} + \frac{1}{{{z^3}}}} \right)^2} + \ldots + {\left( {{z^6} + \frac{1}{{{z^6}}}} \right)^2}$ is

Let $a_1, a_2, \ldots \ldots, a_n$ be in A.P. If $a_5=2 a_3$ and $a_{11}=18$, then $12\left(\frac{1}{\sqrt{a_{10}}+\sqrt{a_{11}}}+\frac{1}{\sqrt{a_{11}}+\sqrt{a_{12}}}+\ldots . \cdot \frac{1}{\sqrt{a_{17}}+\sqrt{a_{18}}}\right)$ is equal to $..........$.

$A(0,2)$ and $C(6,4)$ are opposite vertices of square $ABCD$. Sum of slopes of sides through vertex $A$ will be-

If $^8{C_r}{ = ^8}{C_{r + 2}}$, then the value of $^r{C_2}$ is

Which of the following functions is differentiable at $x = 0$

Assume $X,\, Y,\, Z,\, W$ and $P$ are matrices of order $2 \times n,\, 3 \times k,\, 2 \times p, \,n \times 3$ and $p \times k$ respectively. If $n=p,$ then the order of the matrix $7 X-5 Z$ is

The radius of the circle having its centre at $(0, 3)$ and passing through the foci of the ellipse $\frac{{{x^2}}}{{16}} + \frac{{{y^2}}}{9} = 1$, is

If the variance of observations ${x_1},\,{x_2},\,......{x_n}$ is ${\sigma ^2}$, then the variance of $a{x_1},\,a{x_2}.......,\,a{x_n}$, $\alpha \ne 0$ is

If $\alpha ,\beta $ are the roots of the equation $l{x^2} + mx + n = 0$, then the equation whose roots are ${\alpha ^3}\beta $ and $\alpha {\beta ^3}$ is

Let $A =\{ x \in R :| x +1|<2\}$ and $B=\{x \in R:|x-1| \geq 2\}$. Then which one of the following statements is NOT true ?