Mathematics

# Find the value of the following integral for $a>0$$\int _{ -\pi }^{ \pi }{ \dfrac { \cos { ^{ 2 }x } }{ 1+{ a }^{ x } } dx }$

$\pi/2$

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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 Hard
$\displaystyle \int\frac{\tan x}{\sec x+\cos x}dx=$
• A. $\tan^{-1}(\cos x)+c$
• B. $\tan^{-1} (\sin x)+c$
• C. $-\tan^{-1}(\sin x)+c$
• D. $-\tan^{-1}(\cos x)+c$

1 Verified Answer | Published on 17th 09, 2020

Q2 Single Correct Medium
The value of $\displaystyle\int _{ 0 }^{ { x }/{ 4 } }{ \dfrac { \sec { x } }{ { \left( \sec { x } +\tan { x } \right) }^{ 2 } } dx }$ is
• A. $1+\sqrt{2}$
• B. $-11+\sqrt{2}$
• C. $-\sqrt{2}$
• D. None of these

1 Verified Answer | Published on 17th 09, 2020

Q3 Single Correct Medium
$\displaystyle \int _{0}^{\infty}\dfrac{dx}{(x+\sqrt{x^{2}+1})^{n}}\ (n\ \in \ N)(n\pm 1)$ is
• A. $n(n^{2}-1)$
• B. $\dfrac{n}{(n^{2}-1)}$
• C. $n^{2}$
• D. $0$

1 Verified Answer | Published on 17th 09, 2020

Q4 Subjective Medium
Integrate with respect to $x$:
$\ell n\ x$

Solve$\displaystyle \int_0^1 \dfrac{x^2-2}{x^2+1}dx$