Question
$\int\frac{-1}{\text{y}^2}\text{dy}$ is:
  1. $\frac{1}{\text{y}}$
  2. 1 - y
  3. y
  4. 1 + y

Answer

  1. $\frac{1}{\text{y}}$

Solution:

$\int\frac{-1}{{\text{y}}^2}\text{dy}$

$=-\int\text{y}^{-2}\text{dy}$

$=\text{y}^{-1}=\frac{1}{\text{y}}$

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

${d \over {dx}}\left( {{x^3}{{\tan }^2}{x \over 2}} \right)=$
Choose the correct answer from the given four options.
Projection vector of $\vec{\text{a}}$ on $\vec{\text{b}}$ is:
  1. $\bigg(\frac{\vec{\text{a}}\cdot\vec{\text{b}}}{|\vec{\text{b}}|^2}\bigg)\vec{\text{b}}$
  2. $\frac{\vec{\text{a}}\cdot\vec{\text{b}}}{|\vec{\text{b}}|}$
  3. $\frac{\vec{\text{a}}\cdot\vec{\text{b}}}{|\vec{\text{a}}|}$
  4. $\bigg(\frac{\vec{\text{a}}\cdot\vec{\text{b}}}{|\vec{\text{a}}|^2}\bigg)\vec{\text{b}}$
Let $\alpha$ be a non-zero real number. Suppose $f: \mathrm{R} \rightarrow$ $\mathrm{R}$ is a differentiable function such that $f(0)=2$ and $\lim _{\mathrm{x} \rightarrow-\infty} \mathrm{f}(\mathrm{x})=1$. If $f^{\prime}(\mathrm{x})=\alpha f(x)+3$, for all $\mathrm{x} \in \mathrm{R}$, then $f\left(-\log _e 2\right)$ is equal to . . . . . . . . . 
If $|\vec{a}-\vec{b}|=|\vec{a}|=|\vec{b}|=1$, then the angle between $\vec{a}$ and $\vec{b}$ is
$\int\frac{\sin^2\text{x}-\cos^2\text{x}}{\sin^2\text{x}\cos^2\text{x}}\text{dx}$ is equal to:
  1. $\tan\text{x}+\cos\text{x}+\text{c}$
  2. $\tan\text{x}+\text{cosec}\text{x}+\text{c}$
  3. $\tan\text{x}+\text{cot}\text{x}+\text{c}$
  4. $\tan\text{x}+\sec\text{x}+\text{c}$
If $A$ and $B$ are $3 \times 3$matrices such that $AB = A$ and $BA = B$, then
Let $\vec a\, = \,\hat i\, + \,\hat j\, + \,\sqrt 2 \hat k,\,\,\vec b\, = \,{b_1}\hat i\, + \,{b_2}\hat j\, + \sqrt 2 \hat k$ and $\vec c\, = \,5\hat i\, + \,\hat j + \sqrt 2 \hat k$ be three vectors such that the projection vector of $\vec b$ on $\vec a$ is $\vec a$. If $\vec a\, + \vec b$ is perpendicular to $\vec c$ , then $\left| {\vec b} \right|$ is equal to
The region formed by the inequalities $2 x+3 y-5 \leq 0,4 x-3 y+2 \leq 0$ and $x \geq 0 \ldots \ldots \ldots$
Evaluate: $\int \frac{x-4}{(x-2)^3} \cdot e^x d x$
Let $x =\sin \left(2 \tan ^{-1} \alpha\right)$ and $y =\sin \left(\frac{1}{2} \tan ^{-1} \frac{4}{3}\right)$. If $S =\left\{\alpha \in R : y ^{2}=1- x \right\}$, then $\sum_{\alpha \in S } 16 \alpha^{3}$ is equal to $...........$