Mathematics

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


SOLUTION
View Full Answer

Its FREE, you're just one step away


Subjective Medium Published on 17th 09, 2020
Next Question
Questions 203525
Subjects 9
Chapters 126
Enrolled Students 114
Enroll Now For FREE

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. $$\dfrac { 2 } { 3 }$$

Asked in: Mathematics - Integrals


1 Verified Answer | Published on 17th 09, 2020

View Answer
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.$$\frac{{\cos x - \sin x}}{{1 + \sin 2x}}$$

Asked in: Mathematics - Integrals


1 Verified Answer | Published on 17th 09, 2020

View Answer
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. $$2\left (1-\dfrac {1}{e}\right)$$

Asked in: Mathematics - Integrals


1 Verified Answer | Published on 17th 09, 2020

View Answer
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

Asked in: Mathematics - Integrals


1 Verified Answer | Published on 17th 09, 2020

View Answer
Q5 Passage Medium
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. 
On the basis of above information answer the following questions

Asked in: Mathematics - Integrals


1 Verified Answer | Published on 17th 09, 2020

View Answer