Mathematics

If $\int _{ 0 }^{ k }{ \frac { dx }{ 2+8{ x }^{ 2 } } =\frac { \pi }{ 16 } }$ then k=

$1$

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

Realted Questions

Q1 Single Correct Hard
$\int \left [\displaystyle \frac {\sqrt{x^2\, +\, 1}\, [ln(x^2\, +\, 1)\, -\, 2\, ln\, x]}{x^4} \right ]$
• A. $\displaystyle \frac {(x^2\, -\, 1)\, \sqrt{x^2\, -\, 1}}{9x^3}\, \left [2\, -\, 3\, ln\, \left (1\, +\, \displaystyle \frac {1}{x^2} \right ) \right ]$
• B. $\displaystyle \frac {(x^2\, -\, 1)\, \sqrt{x^2\, -\, 1}}{9x^3}\, \left [2\, +\, 3\, ln\, \left (1\, +\, \displaystyle \frac {1}{x^2} \right ) \right ]$
• C. $\displaystyle \frac {(x^2\, -\, 1)\, \sqrt{x^2\, +\, 1}}{9x^3}\, \left [2\, +\, 3\, ln\, \left (1\, +\, \displaystyle \frac {1}{x^2} \right ) \right ]$
• D. $\displaystyle \frac {(x^2\, +\, 1)\, \sqrt{x^2\, +\, 1}}{9x^3}\, \left [2\, -\, 3\, ln\, \left (1\, +\, \displaystyle \frac {1}{x^2} \right ) \right ]$

1 Verified Answer | Published on 17th 09, 2020

Q2 Single Correct Medium
The value of $\int _{ 0 }^{ \pi /2 }{ \cfrac { \sin { x } -\cos { x } }{ 1+\sin { x } \cos { x } } } dx$ is ____
• A. $\cfrac{\pi}{2}$
• B. $\cfrac{\pi}{4}$
• C. $\pi$
• D. $0$

1 Verified Answer | Published on 17th 09, 2020

Q3 Multiple Correct Hard
If $\displaystyle \int x\log \left ( 1+x^{2} \right )dx=\phi \left ( x \right ).\log \left ( 1+x^{2} \right )+\Psi \left ( x \right )+c$ then
• A. $\displaystyle \Psi \left ( x \right )=\frac{1+x^{2}}{2}$
• B. $\displaystyle \phi \left ( x \right )=-\frac{1+x^{2}}{2}$
• C. $\displaystyle \phi \left ( x \right )=\frac{1+x^{2}}{2}$
• D. $\displaystyle \Psi \left ( x \right )=-\frac{1+x^{2}}{2}$

1 Verified Answer | Published on 17th 09, 2020

Q4 Subjective Medium
Find the value of $\displaystyle \int _{0}^{2}|1-x|\ dx$.

$\int \frac{x}{x^2 + a^2} \;dx$