^ x f(x)+f'(x) dx= 1. e^ x f(x)+C 2. e^ x +f(x) 3. 2e^ x f(x) 4. … - Vidyadip

Question

$\int\text{e}^{\text{x}}\{\text{f(x)}+\text{f}'(\text{x})\}\text{dx}=$

$\text{e}^{\text{x}}\text{f(x)}+\text{C}$
$\text{e}^{\text{x}}+\text{f(x)}$
$2\text{e}^{\text{x}}\text{f(x)}$
$\text{e}^{\text{x}}-\text{f(x)}$

✓

Answer

$\text{e}^{\text{x}}\text{f(x)}+\text{C}$

Solution:

$\int\text{e}^{\text{x}}\{\text{f(x)}+\text{f}'(\text{x})\}\text{dx}=\text{e}^{\text{x}}\text{f(x)}+\text{C}$

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

The differential equation of family of ellipse $\frac{{{x^2}}}{{{a^2}}} + \frac{{{y^2}}}{{{b^2}}}$ = $c$ is $\left( {y' = \frac{{dy}}{{dx}},\,y'' = \frac{{{d^2}y}}{{d{x^2}}}} \right)$

The degree and order of differential equation $y^{\prime \prime 2}+\log \left(y^{\prime}\right)=x^5$ respectively are:

$\int {\frac{{\cos x + x\sin x}}{{x(x - \cos x)}}dx = } $

Let $A$ be a $n \times n$ matrix such that $| A |=2$. If the determinant of the matrix $\operatorname{Adj}\left(2 . \operatorname{Adj}\left(2 A ^{-1}\right)\right.$ ). is $2^{84}$, then $n$ is equal to $................$

The random valuable $X$ follows binomial distribution $B (n, p)$ for which the difference of the mean and the variance is $1$. If $2 P(X=2)=3 P(X=1)$, then $n^2 P(X > 1)$ is equal to $......$.

Let $a$ and $b$ be positive real numbers. Suppose $\overrightarrow{ PQ }=a \hat{ i }+b \hat{ j }$ and $\overrightarrow{ PS }=a \hat{ i }-b \hat{ j }$ are adjacent sides of $a$ parallelogram $P Q R S$. Let $\overrightarrow{ u }$ and $\overrightarrow{ v }$ be the projection vectors of $\overrightarrow{ w }=\hat{ i }+\hat{ j }$ along $\overrightarrow{ PQ }$ and $\overrightarrow{ PS }$, respectively. If $|\vec{u}|+|\vec{v}|=|\vec{w}|$ and if the area of the parallelogram $P Q R S$ is $8$ , then which of the following statements is/are $TRUE$?

$(A)$ $a+b=4$

$(B)$ $a-b=2$

$(C)$ The length of the diagonal $P R$ of the parallelogram $P Q R S$ is $4$

$(D)$ $\overrightarrow{ w }$ is an angle bisector of the vectors $\overrightarrow{ PQ }$ and $\overrightarrow{ PS }$

A vector parallel to the line of intersection of the plance $\vec{\text{r}}.(3\hat{\text{i}}-\hat{\text{j}}+\hat{\text{k}})=1$ and $\vec{\text{r}}.(\hat{\text{i}}-4\hat{\text{j}}+2\hat{\text{k}})=2$ is:

$-2\hat{\text{i}}+7\hat{\text{j}}+13\hat{\text{k}}$
$2\hat{\text{i}}+7\hat{\text{j}}-13\hat{\text{k}}$
$-2\hat{\text{i}}-7\hat{\text{j}}+13\hat{\text{k}}$
$2\hat{\text{i}}+7\hat{\text{j}}+13\hat{\text{k}}$

Minimize Z = 20x₁ + 9x₂, subject to $\text{x}_{1}\geq0,\text{x}_{2}\geq0,2\text{x}_{1}+2\text{x}_{2}\geq36,6\text{x}_{1}+\text{x}_{2}\geq60.$

Smaller area enclosed by the circle x² + y² = 4 and the line x + y = 2 is:

$2(\pi-2)$
$\pi-2$
$\pi-1$
$2(\pi+2)$

The value of the determinant $\left| {\,\begin{array}{*{20}{c}}{31}&{37}&{92}\\{31}&{58}&{71}\\{31}&{105}&{24}\end{array}\,} \right|$ is