Mathematics

# The value of $\displaystyle \int _{ 0 }^{ \pi/2}{ \dfrac { { e }^{ \cos { x } } }{ { e }^{ \cos { x } }+{ e }^{ -\cos { x } } } }$ dx is

$\dfrac{\pi}{4}$

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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
$\displaystyle \int e^x \sec x(1+\tan x)dx$
• A. $e^x\cos x+C$
• B. $e^x\sin x+C$
• C. $e^x\tan x+C$
• D. $e^x\sec x+C$

1 Verified Answer | Published on 17th 09, 2020

Q2 Subjective Medium
Solve: $\int tan (x)dx=?$

1 Verified Answer | Published on 17th 09, 2020

Q3 Single Correct Medium
If $f\left( x \right) =\frac { x }{ 1+(\ln { x } )(\ln { x } ).....\infty } \vee x\in [1,\infty )\quad then\quad \int _{ 1 }^{ 2e }{ f\left( x \right) dx }$ equals is :
• A. $\frac { { e }^{ 2 }+1 }{ 2 }$
• B. $\frac { { e }^{ 2 }-2e }{ 2 }$
• C. None of these
• D. $\frac { { e }^{ 2 }-1 }{ 2 }$

1 Verified Answer | Published on 17th 09, 2020

Q4 Single Correct Medium
lf $\displaystyle \int\frac{2x^{2}+3}{(x^{2}-1)(x^{2}+4)}dx=a\log(\frac{x-1}{x+1})+b\tan^{-1}(\frac{x}{2})+c$, then values of a and $b$ are
• A. $(1, -1)$
• B. $(-1,1)$
• C. $\displaystyle (\frac{1}{2},-\frac{1}{2})$
• D. $\displaystyle (\frac{1}{2},\frac{1}{2})$

1 Verified Answer | Published on 17th 09, 2020

Q5 Subjective Easy
$\int \frac{2x^{2}}{3x^{4}2x} dx$