If dx=-x +a, then a is equal to:

MCQ

If $\int\text{x}\sin\text{x dx}=-\text{x}\cos\text{x}+\text{a},$ then a is equal to:

✓
$\sin\text{x}+\text{C}$
B
$\cos\text{x}+\text{C}$
C
$\text{C}$
D
none of these.

✓

Answer

Correct option: A.

$\sin\text{x}+\text{C}$

$\int\text{x}\sin\text{x dx}=-\text{x}\cos\text{x}+\text{a}$
$\text{I}=\int\text{x}\sin\text{x dx}$
$\text{I}=\text{x}\int\sin\text{x dx}-\int\Big(\frac{\text{dx}}{\text{dx}}\int\sin\text{x dx}\Big)\text{dx}$
$\text{I}=-\text{x}\cos\text{x}+\int\cos\text{x dx}$
$\text{I}=\text{x}\cos\text{x}+\sin\text{x}+\text{C}$
$\text{a}=\sin\text{x}+\text{C}$

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

Similar questions

$\int_{}^{} {\sin (\log x)dx = } $

→

Let the function $f: R \rightarrow R$ be defined by

$f(t)=\left\{\begin{array}{cc}(-1)^{n+1} 2, & \text { if } t=2 n-1, n \in N , \\ \frac{(2 n+1-t)}{2} f(2 n-1)+\frac{(t-(2 n-1))}{2} f(2 n+1), & \text { if } 2 n-1 < t < 2 n+1, n \in N \end{array}\right.$

Define $g(x)=\int_1^x f(t) d t, x \in(1, \infty)$. Let $\alpha$ denote the number of solutions of the equation $g(x)=0$ in the interval $(1,8]$ and $\beta=\lim _{x \rightarrow 1+} \frac{g(x)}{x-1}$. Then the value of $\alpha+\beta$ is equal to. . . . . .

→

The position vectors of P and Q are respectively a and b.If R is a point on PQ, PQ such that PR = 5PQ, then the position vector of R is:

→

If $A$ is a square matrix of order $3$ and $|A| = 5$, then the value of $|2A\ '|$ is:

→

$R$ is a relation from $\{11, 12, 13\}$ to $\{8, 10, 12\}$ defined by $y = x - 3$. Then, $R^{-1}$ is:

→

Two squares are chosen at random on a chess-board. The probability that they have a side in common, is

→

On the power set P of a non-empty set A, we define an operation $\triangle \text{ by }\text{X}\triangle\text{Y}=(\text{X}\cap\text{Y})∪(\text{X}∩\text{Y})\text{X}\triangle\text{Y}=\text{X}∩\text{Y}∪\text{X}∩\text{Y}$
Then which are of the following statements is true about $\triangle$

→

If $A B C D$ is a rhombus, whose diagonals intersect at $E$, then $\overrightarrow{E A}+\overrightarrow{E B}+\overrightarrow{E C}+\overrightarrow{E D}$ equals