MCQ
If $\frac{\text{dy}}{\text{dx}}=\text{x}^{-3}$ then $y:$
  • $\frac{-1}{2\text{x}^{2}}+\text{c}$
  • B
    $\frac{-\text{x}^{-4}}{4}+\text{c}$
  • C
    $\frac{2}{\text{x}^{2}}+\text{c}$
  • D
    $\frac{\text{x}^{-2}}{2}+\text{c}$

Answer

Correct option: A.
$\frac{-1}{2\text{x}^{2}}+\text{c}$

we have $\frac{\text{dy}}{\text{dx}}=\text{x}^{-3}$
$\Rightarrow dy = x^{-3} dx$
Integrating both sides 
$\therefore\text{y}=\int\text{x}^{-3}\text{dx}=\frac{\text{x}^{-3 + 1}}{-3+1}+\text{c}=-\frac{1}{2\text{x}^2}+\text{c}$

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

Similar questions

Evaluate: $\int_0^2(x-[x]) d x$
The number of functions defined from $\{1,2,3,4,5\} \rightarrow\{a, b\}$ which are one-one is
If $A, B$ are square matrices of order $3, A$ is non-singular and $AB = 0$ then $B$ is a
Let $\text{U}=\sin^{-1}\Big(\frac{2\text{x}}{1+\text{x}^2}\Big)$ and $\text{V}=\tan^{-1}\Big(\frac{2\text{x}}{1-\text{x}^2}\Big),$ then $\frac{\text{dU}}{\text{dV}}=$
  1. $\frac{1}{2}$
  2. $\text{x}$
  3. $\frac{1-\text{x}^2}{\text{x}^2-4}$
  4. $1$
If $\text{S}=\begin{bmatrix}\text{a} & \text{b} \\ \text{c} & \text{d} \end{bmatrix},$ then adj A is:
  1. $\begin{bmatrix} -\text{d} & -\text{b} \\ -\text{c} & \text{a} \end{bmatrix}$
  2. $\begin{bmatrix} \text{d} & -\text{b} \\ -\text{c} & \text{a} \end{bmatrix}$
  3. $\begin{bmatrix} \text{d} & \text{b} \\ \text{c} & \text{a} \end{bmatrix}$
  4. $\begin{bmatrix} \text{d} & \text{c} \\ \text{b} & \text{a} \end{bmatrix}$
Subtraction of integers is:
  1. Commutative but no associative.
  2. Commutative and associative.
  3. Associative but not commutative.
  4. Neither commutative nor associative.
The corner points of the feasible region determined by the system of linear constraints are (0, 10), (5, 5), (15, 15), (0, 20). Let Z = px + qy, where p, q > 0. Condition on p and q so that the maximum of Z occurs at both the points (15, 15) and (0, 20) is
If P(A) + P(B) = 1; then which of the following option explains the event A and B correctly?
  1. Event A and B are mutually exclusive, exhaustive and complementary events.
  2. Event A and B are mutually exclusive and exhaustive events.
  3. Event A and B are mutually exclusive and complementary events.
  4. Event A and B are exhaustive and complementary events.
$\int \frac{d x}{x \log _e x}$ is equal to :
The vector equation of the plane passing through $\vec{\text{a}},\ \vec{\text{b}},\ \vec{\text{c}},$ is $\vec{\text{r}}=\alpha\vec{\text{a}}+\beta\vec{\text{b}}+\gamma\vec{\text{c}}$, provided that,
  1. $\alpha+\beta+\gamma=0$
  2. $\alpha+\beta+\gamma=1$
  3. $\alpha+\beta=\gamma$
  4. $\alpha^2+\beta^2+\gamma^2=1$