Mathematics

# If $\underset{0}{\overset{1}{\int}} tan^{-1} (1 - x + x^2) dx$ equals

$In \, 2$

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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 Medium
The value of $\displaystyle\int { \dfrac { dx }{ \left( 1+{ x }^{ 2 } \right) \sqrt { 1-{ x }^{ 2 } } } }$ is
• A. $\dfrac { 1 }{ \sqrt { 2 } } \tan ^{ -1 }{ \left( \dfrac { \sqrt { 1-{ x }^{ 2 } } }{ \sqrt { 2 } x } \right) } +C$
• B. $- \tan ^{ -1 }{ \left( \dfrac { \sqrt { 1-{ x }^{ 2 } } }{ \sqrt { 2 } x } \right) } +C$
• C. None of the above
• D. $-\dfrac { 1 }{ \sqrt { 2 } } \tan ^{ -1 }{ \left( \dfrac { \sqrt { 1-{ x }^{ 2 } } }{ \sqrt { 2 } x } \right) } +C$

1 Verified Answer | Published on 17th 09, 2020

Q2 Subjective Medium
Evaluate: $\displaystyle\int {\frac{{1 - \cot x}}{{1 + \cot x}}dx}$

1 Verified Answer | Published on 17th 09, 2020

Q3 Single Correct Medium
$\displaystyle \int \dfrac{(a^{x}-b^{x})^{2}}{a^{x}b^{x}}dx$ equals
• A. $(b/a)^{x}+2x+c$
• B. $(a/b)^{x}-2x+c$
• C. $None\ of\ these$
• D. $(a/b)^{x}+2x+c$

1 Verified Answer | Published on 17th 09, 2020

Q4 Subjective Medium
Solve:$\displaystyle \int_0^{2\pi}\dfrac{\cos x }{1+\sin^2 x} dx$

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