Mathematics

# Using integral $\int _{ 0 }^{ \pi /2 }{ \ln { \left( \sin { x } \right) } } dx=\int _{ 0 }^{ \pi /2 }{ \ln { \left( \sec { x } \right) } } dx=-\cfrac { \pi }{ 2 } \ln { 2 }$Evaluate $\int _{ -\pi /4 }^{ \pi /4 }{ \ln { \left( \cfrac { \sin { x } +\cos { x } }{ \cos { x } -\sin { x } } \right) } dx= }$

$0$

Its FREE, you're just one step away

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

#### Realted Questions

Q1 Subjective Medium
Evaluate $\displaystyle\int^{\pi/3}_0\tan x dx$.

1 Verified Answer | Published on 17th 09, 2020

Q2 Subjective Medium
Evaluate the following integral
$\int { \cfrac { \cos { x } }{ \cos { \left( x-a \right) } } } dx\quad$

1 Verified Answer | Published on 17th 09, 2020

Q3 Single Correct Medium
$\int \dfrac{f(x)g'(x)-f'(x)g(x)}{f(x)g(x)} \left [ log(g(x))-log(f(x)) \right ]dx=$
• A. $\log (\dfrac{g(x)}{f(x)} )+C$
• B. $\dfrac{(g)x}{f(x)}\log(\dfrac{g(x)}{f(x)} )+C$
• C. $\log\left [ \dfrac{g(X)}{f(X)} \right ]-\dfrac{g(x)}{f(x)}+C$
• D. $\dfrac{1}{2} \left [ log(\dfrac{g(x)}{f(x)} ) \right ]^{2}+C$

1 Verified Answer | Published on 17th 09, 2020

Q4 Subjective Medium
By using the properties of definite integrals, evaluate the integral   $\displaystyle \int_0^2x\sqrt {2-x}dx$

Evaluate $\int \dfrac {1}{\sqrt {7-6x-{x}^{2}}}$