Mathematics

# If $f(x) =\displaystyle \underset{1}{\overset{x}{\int}} \dfrac{\tan^{-1} t}{t} dt \, \, \forall \in R$, then the value of $f(e^2) - f \left (\dfrac{1}{e^2}\right)$is

$\pi$

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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
If $\int {\frac{{\sin x}}{{\sin \left( {x - \alpha } \right)}}dx} = Ax + B\log \sin \left( {x - \alpha } \right) + C$, then value of $\left( {A,B} \right)$ is
• A. $\left( {-\sin \alpha ,-cos\alpha } \right)$
• B. $\left( { - \cos \alpha ,sin\alpha } \right)$
• C. $\left( { - \sin \alpha ,cos\alpha } \right)$
• D. $\left( {\cos \alpha ,sin\alpha } \right)$

1 Verified Answer | Published on 17th 09, 2020

Q2 Subjective Medium
Evaluate : $\displaystyle \int_{0}^{1}\dfrac {2x + 3}{5x^{2} + 1} dx$

1 Verified Answer | Published on 17th 09, 2020

Q3 Single Correct Medium
Show that:
$\int_{ - 1}^1 {{x^{17}}{{\cos }^{4\,}}xdx = 0}$.
• A. 2
• B. 1
• C. 3
• D.

1 Verified Answer | Published on 17th 09, 2020

Q4 Subjective Hard
Evaluate:$\int _{ 1 }^{ 3 }{ \left( { x }^{ 2 }+3 \right)^{ 2 }dx }$

1 Verified Answer | Published on 17th 09, 2020

Q5 Single Correct Medium
$\int_{-1}^{1}x^{17}\ \cos^{4}\ x\ dx$ is equals to
• A. $-2$
• B. $2$
• C. $1$
• D. $0$