Mathematics

# The value of the integral $\int _ { 0 } ^ { \pi / 2 } \frac { 1 + 2 \cos x } { ( 2 + \cos x ) ^ { 2 } } d x$ is

$\frac { -1 } { 2 }$

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Single Correct Hard Published on 17th 09, 2020
Questions 203525
Subjects 9
Chapters 126
Enrolled Students 114

#### Realted Questions

Q1 Subjective Medium
Evaluate $\displaystyle\int { \cfrac { 2\cos { x } -3\sin { x } }{ 6\cos { x } +4\sin { x } } } dx$

1 Verified Answer | Published on 17th 09, 2020

Q2 Single Correct Hard
If $\int \dfrac {dx}{\cos^{3} x\sqrt {2\sin 2x}} = (\tan x)^{A} + C(\tan x)^{B} + k$, where $k$ is a constant of integration, then the value of $A + B + C$ is equal to:
• A. $\dfrac {21}{5}$
• B. $\dfrac {21}{10}$
• C. $\dfrac {7}{10}$
• D. $\dfrac {16}{5}$

1 Verified Answer | Published on 17th 09, 2020

Q3 Single Correct Medium
What is $\displaystyle \int _{ 0 }^{ 1 }{ \cfrac { \tan ^{ -1 }{ x } }{ 1+{ x }^{ 2 } } } dx$ equal to?
• A. $\cfrac { { \pi }^{ 2 } }{ 8 }$
• B. $\cfrac { \pi }{ 4 }$
• C. $\cfrac { \pi }{ 8 }$
• D. $\cfrac { { \pi }^{ 2 } }{ 32 }$

1 Verified Answer | Published on 17th 09, 2020

Q4 Subjective Medium
$\displaystyle \int \frac { \sec ^2x } { 1 + \tan x } \cdot d x$

$\int_{}^{} {\frac{{ - 1}}{{\sqrt {1 - {x^2}} }}dx}$