Mathematics

# The value of $\displaystyle \underset{0}{\overset{x}{\int}} \dfrac{(t - |t|)^2}{(1 + t^2)} dt$ is equal to

Its FREE, you're just one step away

One Word Medium Published on 17th 09, 2020
Questions 203525
Subjects 9
Chapters 126
Enrolled Students 84

#### Realted Questions

Q1 Single Correct Medium
If $\displaystyle \frac{ax}{(x+2)(x-1)} = \frac{2}{x+2}+\frac{1}{x-1}$, then a =
• A. $1$
• B. $2$
• C. $4$
• D. $3$

1 Verified Answer | Published on 17th 09, 2020

Q2 Single Correct Hard
The value of $\displaystyle \lim_{n \rightarrow \infty} e^{\frac{3i}{n}} \cdot \dfrac{3}{n} = ?$
• A. $e^4 -1$
• B. $e^5 -1$
• C. $e^3 -2$
• D. $e^3 -1$

1 Verified Answer | Published on 17th 09, 2020

Q3 Subjective Medium
Evaluate the following integral
$\int { \cfrac { 1 }{ x\log { x } } } dx$

1 Verified Answer | Published on 17th 09, 2020

Q4 Single Correct Medium
$\displaystyle \int { \frac { \cos { x } +x\sin { x } }{ x\left( x+\cos { x } \right) } dx }$ is equal to
• A. $\displaystyle \log { \left| \frac { x+\cos { x } }{ x } \right| +c }$
• B. $\displaystyle \log { \left| \frac { 1 }{ x+\cos { x } } \right| +c }$
• C. $\log { \left| x+\cos { x } \right| +c }$
• D. $\displaystyle \log { \left| \frac { x }{ x+\cos { x } } \right| +c }$

1 Verified Answer | Published on 17th 09, 2020

Q5 Passage Hard
Let us consider the integral of the following forms
$f{(x_1,\sqrt{mx^2+nx+p})}^{\tfrac{1}{2}}$
Case I If $m>0$, then put $\sqrt{mx^2+nx+C}=u\pm x\sqrt{m}$
Case II If $p>0$, then put $\sqrt{mx^2+nx+C}=u\pm \sqrt{p}$
Case III If quadratic equation $mx^2+nx+p=0$ has real roots $\alpha$ and $\beta$, then put $\sqrt{mx^2+nx+p}=(x-\alpha)u\:or\:(x-\beta)u$