Mathematics

# $\underset{0}{\overset{\pi}{\int}} \log (1 + \cos \, x) dx =$

$-\dfrac{\pi}{2} \log 2$

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Single Correct Medium Published on 17th 09, 2020
Questions 203525
Subjects 9
Chapters 126
Enrolled Students 86

#### Realted Questions

Q1 Subjective Medium
$\text { Evaluate: } \displaystyle \int_{0}^{\pi} \dfrac{x \tan x}{\sec x \cdot \operatorname{cosec} x} d x$

1 Verified Answer | Published on 17th 09, 2020

Q2 Single Correct Medium
Obtain $\displaystyle \int _{ 0 }^{ \pi }{ \sqrt { 1+\cos { 2x } } dx }$
• A. $2$
• B. $12$
• C. None of these
• D. $0$

1 Verified Answer | Published on 17th 09, 2020

Q3 Single Correct Hard
Evaluate $\displaystyle \int_{0}^{\pi /4}\frac{\cos x-\sin x}{10+\sin 2x}dx$
• A. $\displaystyle \frac{1}{3}\left (\tan^{-1} \frac{\sqrt{2}}{3}+\tan^{-1} \frac{1}{3} \right )$
• B. $\displaystyle \frac{1}{3}\left (\tan^{-1} \frac{\sqrt{1}}{3}-\cot^{-1} \frac{2}{3} \right )$
• C. $\displaystyle \frac{1}{3}\left ( \tan^{-1} \frac{\sqrt{1}}{3}-\cot^{-1} \frac{1}{3} \right )$
• D. $\displaystyle \frac{1}{3}\left ( \tan^{-1} \frac{\sqrt{2}}{3}-\tan^{-1} \frac{1}{3} \right )$

1 Verified Answer | Published on 17th 09, 2020

Q4 Subjective Medium
$\displaystyle\int \left(e^x\right)^2 e^x dx$ is equal to

$\int { \cfrac { f'(x) }{ f(x) } dx } =\log { [f(x)] } +c$