Mathematics

# Evaluate the following integrals$\int { \cfrac { 1 }{ \sin { x } +\sqrt { 3 } \cos { x } } } dx$

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Subjective Medium Published on 17th 09, 2020
Questions 203525
Subjects 9
Chapters 126
Enrolled Students 114

#### Realted Questions

Q1 Single Correct Medium
The correct evaluation of $\displaystyle \int _ { 0 } ^ { \pi / 2 } \sin x \sin 2 x$ is
• A. $\dfrac { 4 } { 3 }$
• B. $\dfrac { 1 } { 3 }$
• C. $\dfrac { 3 } { 4 }$
• D. $\dfrac { 2 } { 3 }$

1 Verified Answer | Published on 17th 09, 2020

Q2 Subjective Hard
Find the integrals of the functions in Exercises 1 to 22
1. ${\sin ^3}\left( {2x + 1} \right)$
2. $\,{\sin ^3}x{\cos ^3}x$
3.$\frac{{\cos x - \sin x}}{{1 + \sin 2x}}$

1 Verified Answer | Published on 17th 09, 2020

Q3 Single Correct Medium
$\displaystyle \int_{1/e}^{e}{|\ln x|dx}$ equals
• A. $e^{-1}-1$
• B. $1-\dfrac {1}{e}$
• C. $e-1$
• D. $2\left (1-\dfrac {1}{e}\right)$

1 Verified Answer | Published on 17th 09, 2020

Q4 Single Correct Hard
Let $\displaystyle f\left ( x \right )$ be a continuous function such that $\displaystyle f\left ( x \right )$does not vanish for all $\displaystyle x \epsilon R.$ If $\displaystyle \int_{2}^{3}f\left ( x \right )dx= \int_{-2}^{3}$ $\displaystyle f\left ( x \right ) dx$ then $\displaystyle x\epsilon R,$ is
• A. an even function
• B. a periodic function
• C. none of these
• D. an odd function

Let $n \space\epsilon \space N$ & the A.M., G.M., H.M. & the root mean square of $n$ numbers $2n+1, 2n+2, ...,$ up to $n^{th}$ number are $A_{n}$, $G_{n}$, $H_{n}$ and $R_{n}$ respectively.