Mathematics

# $\displaystyle \int _{-\pi/2}^{\pi/2}\dfrac{\cos{x}}{1+e^{x}}\ dx=$

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

#### Realted Questions

Q1 Single Correct Medium
Let $\displaystyle \frac{d}{dx}F\left ( x \right )=\frac{e^{\sin x}}{x},x> 0.$ If $\displaystyle \int_{1}^{4}\frac{2e^{\sin x^{2}}}{x}dx=F\left ( k \right )-F\left ( 1 \right )$ then one of the possible values of $\displaystyle k$ is
• A. $4$
• B. $\displaystyle -4$
• C. none of these
• D. $16$

1 Verified Answer | Published on 17th 09, 2020

Q2 Single Correct Medium
Evaluate $\displaystyle \int \dfrac{1}{1+3\sin^{2}{x}+8\cos^{2}{x}}dx$
• A. $\tan^{-1}{(2\tan{x})}+C$
• B. $\dfrac{1}{6}\tan^{-1}\dfrac{2\tan{x}}{3}+C$
• C. $None\ of\ these$
• D. $\dfrac{1}{6}\tan^{-1}{(2\tan{x})}+C$

1 Verified Answer | Published on 17th 09, 2020

Q3 Subjective Hard
Solve $\displaystyle \int_{0}^{\dfrac{\pi}{4}} \sin 2x\ dx$

1 Verified Answer | Published on 17th 09, 2020

Q4 Subjective Medium
Evaluate
$\int \dfrac{cos \ x}{\sqrt{1+\sin x}}dx$

Evaluate $\int \dfrac{e^x-e^{-x}}{e^x+e^{-x}}dx$