Mathematics

# The value of $\int_{-1}^{3}[tan^{-1}(\frac{x}{x^{2}+1})+tan^{-1}(\frac{x^{2}}{x})]dx$

2$\pi$

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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
$\int { \cfrac { { x }^{ 2 } }{ (9+4{ x }^{ 2 }) } } dx=$?
• A. $\cfrac { x }{ 4 } -\cfrac { 1 }{ 8 } \tan ^{ -1 }{ \cfrac { x }{ 3 } } +C$
• B. $\cfrac { x }{ 4 } -\cfrac { 3 }{ 8 } \tan ^{ -1 }{ \cfrac { x }{ 3 } } +C$
• C. none of these
• D. $\cfrac { x }{ 4 } -\cfrac { 3 }{ 8 } \tan ^{ -1 }{ \cfrac { 2x }{ 3 } } +C$

1 Verified Answer | Published on 17th 09, 2020

Q2 Subjective Hard
Solve $\displaystyle\int \dfrac {dx}{\sin x+\sec x}$

1 Verified Answer | Published on 17th 09, 2020

Q3 Single Correct Medium
$\displaystyle\int { \dfrac { { x }^{ n-1 } }{ { x }^{ 2n }+{ a }^{ 2 } } dx }$ is equal to
• A. $\dfrac { 1 }{ na } \tan ^{ -1 }{ \left( \dfrac { { x }^{ n } }{ a } \right) } +C$
• B. $\dfrac { n }{ a } \sin ^{ -1 }{ \left( \dfrac { { x }^{ n } }{ a } \right) } +C$
• C. $\dfrac { n }{ a } \cos ^{ -1 }{ \left( \dfrac { { x }^{ n } }{ a } \right) } +C$
• D. $\dfrac { 1 }{ na } \cot ^{ -1 }{ \left( \dfrac { { x }^{ n } }{ a } \right) } +C$
• E. $\dfrac { n }{ a } \tan ^{ -1 }{ \left( \dfrac { { x }^{ n } }{ a } \right) } +C$

1 Verified Answer | Published on 17th 09, 2020

Q4 Single Correct Medium
Let $f:R\rightarrow R$ and $g:R\rightarrow R$  be continuous functions, then the value of $\displaystyle\int_{\displaystyle-\frac{\pi}{2}}^{\displaystyle\frac{\pi}{2}}{(f(x)+f(-x))(g(x)-g(-x))dx}$, is equal to
• A. $-1$
• B. $1$
• C. none of these
• D. $0$

$\int { \cfrac { f'(x) }{ f(x) } dx } =\log { [f(x)] } +c$