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

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

Let $f(x) = \left\{ {\begin{array}{*{20}{c}}
{{x^2}\ln x,\,x > 0} \\
{0,\,\,\,\,\,\,\,\,\,\,\,\,\,x = 0}
\end{array}} \right\}$, Rolle’s theorem is applicable to $ f $ for $x \in [0,1]$, if $\alpha = $

If $A$ is a $3 \times 3$ matrix and det$(3A) = k($det $A),$ then $k =$

If $ x=-1 $ and $ x=2 $ are extreme point of $f\left( x \right) = \alpha \log \left| x \right| + \beta {x^2} + x$ then $\left( {\alpha ,\beta } \right)$

Choose the correct answer in Exercise : $\int\text{x}^2\text{e}^{\text{x}^3}\text{dx}$ equals

What is the degree of the differential equation $y =x \frac{d y}{d x}+\left(\frac{d y}{d x}\right)^{-1} ?$

$a\times [a\times (a\times b)]$ is equal to

Let $\vec{v}$ be a vector in the plane such that $| v - i |=| v -2 i |=| v - j |$. Then, $| v |$ lies in the interval

The area bounded by the curves $|x| + |y| \geq 1$ and $x^2 + y^2 \geq 1$ is

The value of a for which the function $\text{f(x)}=\begin{cases}\frac{(4^\text{x}-1)^3}{\sin\Big(\frac{\text{x}}{\text{a}}\Big)\log\Big\{\Big(1+\frac{\text{x}^2}{3}\Big)\Big\}},&\text{x}\neq0\\12(\log4)^3,&\text{x}=0\end{cases}$ may be continuous at x = 0 is:

For the function $\text{f}(\text{x})=\text{x}+1\text{x},\text{x}\in[1,3],$ the value of c for the Lagrange's mean value theorem is: