Mathematics

# The value of ${\int}_{0}^{\pi/2}\dfrac{\sin x dx}{1+\cos x+\sin x}=$

$\dfrac{\pi}{4}$

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Single Correct Medium Published on 17th 09, 2020
Questions 203525
Subjects 9
Chapters 126
Enrolled Students 84

#### Realted Questions

Q1 Subjective Medium
Evaluate $\int$ $\dfrac{1}{(e^x -1)}dx$

1 Verified Answer | Published on 17th 09, 2020

Q2 Subjective Medium
Find the integrals of the function   $\displaystyle \dfrac {\cos x-\sin x}{1+\sin 2x}$

1 Verified Answer | Published on 17th 09, 2020

Q3 Single Correct Hard
$\displaystyle \int { \cfrac { { x }^{ 2 }+1 }{ { x }^{ 4 }+1 } } dx=\quad$?
• A. $\cfrac { 1 }{ 2 } \tan ^{ -1 }{ \left( \cfrac { { x }^{ 2 }+1 }{ \sqrt { 2 } x } \right) } +C\quad$
• B. $\cfrac { 1 }{ \sqrt { 2 } } \log { \left( \cfrac { { x }^{ 2 }+1 }{ { x }^{ 2 }-1 } \right) } +C\quad \quad \quad$
• C. none of these
• D. $\cfrac { 1 }{ \sqrt2 } \tan ^{ -1 }{ \left( \cfrac { { x }^{ 2 }-1 }{ \sqrt { 2 } x } \right) } +C$

1 Verified Answer | Published on 17th 09, 2020

Q4 Single Correct Medium
$\int \frac{e^{x}(x-1)(x-1nx)}{x^{2}}dx$ is equal to
• A. $e^{x}(\frac{x-1n x+1}{x})+c$
• B. $e^{x}(\frac{x-1n x}{x^{2}})+c$
• C. $e^{x}(\frac{x-1n x-1}{x})+c$
• D. $e^{x}(\frac{x-1n x}{x})+c$

$\displaystyle\int\limits_{-1}^{1}xe^{x^2}\ dx$.