Mathematics

# If $\displaystyle I = \int_{0}^{\pi/2} \ln (\sin x) dx$ then $\displaystyle \int_{-\pi/4}^{\pi/4} \ln (\sin x + \cos x) dx =$

$I$

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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

$\displaystyle \int_{0}^{1}\frac{\sqrt{x}}{1+x}dx_{=}$
• A. $1-\pi/2$
• B. $\pi/2$
• C. $2+\pi/2$
• D. $2-\pi/2$

1 Verified Answer | Published on 17th 09, 2020

Q2 Subjective Medium
Evaluate the following integral:
$\displaystyle\int_{-4}^{4}|x+2|\ dx$

1 Verified Answer | Published on 17th 09, 2020

Q3 Single Correct Medium
$\displaystyle \int \dfrac {\sin x + \cos x}{e^{-x} + \sin x} dx$ is equal to
• A. $\log |1 - e^{x}\sin x| + C$
• B. $\log |1 + e^{-x}\sin x| + C$
• C. $\log |1 - e^{-x}\sin x| + C$
• D. $\log |1 + e^{2x}\sin x| + C$
• E. $\log |1 + e^{x}\sin x| + C$

1 Verified Answer | Published on 17th 09, 2020

Q4 Single Correct Medium
$\int { \cfrac { \cos { x } -1 }{ \sin { x } +1 } } { e }^{ x }dx$ is equal to:
• A. $c-\cfrac { { e }^{ x }\sin { x } }{ 1+\sin { x } }$
• B. $c-\cfrac { { e }^{ x }}{ 1+\sin { x } }$
• C. $c-\cfrac { { e }^{ x }\cos { x } }{ 1+\sin { x } }$
• D. $\cfrac { { e }^{ x }\cos { x } }{ 1+\sin { x } } +c$

Let $\displaystyle f\left ( x \right )=\frac{\sin 2x \cdot \sin \left ( \dfrac{\pi }{2}\cos x \right )}{2x-\pi }$