Question
$\int_{0}^{1}\frac{\text{x}}{1+\text{x}}\text{dx}=$
  1. $1-\log2$
  2. $2$
  3. $1+\log 2$
  4. $\log2$

Answer

  1. $1-\log2$

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

What will be the value of $k$ for which $f(x)=$
$\left\{\begin{array}{c}\frac{\sin 3 x}{x}, x \neq 0 \\ k \quad, x=0\end{array}\right.$ is continuous at $x=0$.
The differential equation for $\text{y}=\text{A}\cos\text{ax}+\text{B}\sin\text{ax}$ where A and B are arbitary constants is:
  1. $\frac{\text{d}^2\text{y}}{\text{dx}^2}-\text{a}^2\text{y}=0$
  2. $\frac{\text{d}^2\text{y}}{\text{dx}^2}+\text{a}^2\text{y}=0$
  3. $\frac{\text{d}^2\text{y}}{\text{dx}^2}+\text{ay}=0$
  4. $\frac{\text{d}^2\text{y}}{\text{dx}^2}-\text{ay}=0$
If the solution curve of the differential equation $\left(2 x-10 y^{3}\right) d y+y d x=0$, passes through the points $(0,1)$ and $(2, \beta)$, then $\beta$ is a root of the equation:
Let $[t]$ denote the greatest integer less than or equal to $t$. Let $\mathrm{f}:[0, \infty) \rightarrow \mathrm{R}$ be a function defined by $f(x)=\left[\frac{x}{2}+3\right]-[\sqrt{x}]$. Let $S$ be the set of all points in the interval $[0,8]$ at which $\mathrm{f}$ is not continuous. Then $\sum_{\mathrm{a} \in \mathrm{S}} \mathrm{a}$ is equal to............
Conclude from the following: n2 > 10, and n is a positive integer. A: n3 B: 50.
  1. The quantity A is may be greater or smaller than B.
  2. The quantity B is greater than A.
  3. The two quantities are equal.
  4. The relationship cannot be determined from the information given.
Minimize Z = 20x1 + 9x2, subject to $\text{x}_{1}\geq0,\text{x}_{2}\geq0,2\text{x}_{1}+2\text{x}_{2}\geq36,6\text{x}_{1}+\text{x}_{2}\geq60.$
The number of real solutions of $x^{7}+5 x^{3}+3 x+1=$ $0$ is equal to............
The function $f (x) = sin^4x + cos^4x$ increases if :
The area of the region bounded by the ellipse $\frac{x^2}{16}+\frac{y^2}{9}=1$ is _________ sq. unit.
If $y = {\left( {x + \sqrt {1 + {x^2}} } \right)^n},$ then $(1 + {x^2}){{{d^2}y} \over {d{x^2}}} + x{{dy} \over {dx}}$ is