Mathematics

The value of $\displaystyle \int _{ -\dfrac { \pi }{ 2 } }^{ 2 }{ \dfrac { \sin ^{ 2 }{ x } }{ 1+{ 2 }^{ x } } } dx$ is:

$\dfrac {\pi}{4}$

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Single Correct Medium Published on 17th 09, 2020
Questions 203525
Subjects 9
Chapters 126
Enrolled Students 86

Realted Questions

Q1 Single Correct Medium
The integral $\displaystyle\int \dfrac{dx}{x^2(x^4+1)^{3/4}}$ equals?
• A. $(x^4+1)^{1/4}+C$
• B. $-(x^4+1)^{1/4}+C$
• C. $-\left(\dfrac{x^4+1}{x^4}\right)^{1/4}+C$
• D. $\left(\dfrac{x^4+1}{x^4}\right)^{1/4}+C$

1 Verified Answer | Published on 17th 09, 2020

Q2 Single Correct Hard
$\displaystyle \int \dfrac{\sec^2 x}{(\sec x + \tan x)^{9/2}} dx$ equals
• A. $- \dfrac{1}{(\sec x + \tan x)^{11/2}} \left \{ \dfrac{1}{11} - \dfrac{1}{7} (\sec x + \tan x)^2 \right \} + K$
• B. $\dfrac{1}{(\sec x + \tan x)^{11/2}} \left \{ \dfrac{1}{11} - \dfrac{1}{7} (\sec x + \tan x)^2 \right \} + K$
• C. None of the above
• D. $-\dfrac{1}{(\sec x + \tan x)^{11/2}} \left \{ \dfrac{1}{11} + \dfrac{1}{7} (\sec x + \tan x) \right \} + K$

1 Verified Answer | Published on 17th 09, 2020

Q3 Single Correct Medium
The value of $\int { { x }^{ 3 }\log { x } dx }$ is
• A. $\dfrac { 1 }{ 8 } \left( { x }^{ 4 }\log { x } -4{ x }^{ 4 }+c \right)$
• B. $\dfrac { 1 }{ 16 } \left( 4{ x }^{ 4 }\log { x } +{ x }^{ 4 }+c \right)$
• C. $\dfrac { { x }^{ 4 }\log { x } }{ 4 } +c$
• D. $\dfrac { 1 }{ 16 } \left( 4{ x }^{ 4 }\log { x } -{ x }^{ 4 }+c \right)$

1 Verified Answer | Published on 17th 09, 2020

Q4 Subjective Hard
Evaluate:$\displaystyle\int{\sqrt{\dfrac{1-\sqrt{x}}{1+\sqrt{x}}}\dfrac{dx}{x}}$

1 Verified Answer | Published on 17th 09, 2020

Q5 Single Correct Hard
If $\displaystyle I = \int tan^{-1} \sqrt {\left ( \sqrt x - 1 \right )} dx = (u^2 + 1)^2 tan^{-1} u - \frac {A}{1863} u^3 - u + C$ where $\displaystyle u = \sqrt {\sqrt x - 1}$ then A is equal to.
• A. 312
• B. 316
• C. 318
• D. 321