Mathematics

Evaluate the following definite integral :
$$\displaystyle \int _{\pi /6}^{\pi /4}  \ \text{cosec} \  x \ dx$$ 


SOLUTION
Now,
$$\displaystyle \int _{\pi /6}^{\pi /4}  \ \text{cosec} \  x \ dx$$ 

$$=\left[\log|(cosec x-\cot x)|\right]_{\tfrac{\pi}{4}}^{\tfrac{\pi}{6}}$$ [ Using direct formula]

$$=\log|(2-\sqrt{3})|-\log|(\sqrt{2}-1)|$$

$$=\log\left|\dfrac{2-\sqrt3}{\sqrt2-1}\right|$$
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 86
Enroll Now For FREE

Realted Questions

Q1 Multiple Correct Medium
If $$f\left( x \right)$$ satisfies the relation $$f\left( \dfrac { 5x-3y }{ 2 }  \right) =\dfrac { 5f\left( x \right) -3f\left( y \right)  }{ 2 } \forall \ x,y\in R$$ and $$\ f\left( 0 \right) =3$$ and $$f^{ ' }\left( 0 \right) =2$$, then the period of $$\sin { \left( f\left( x \right)  \right)  }$$ is
  • A. $$2\pi$$
  • B. $$4\pi$$
  • C. $$\pi$$
  • D. $$3\pi$$

Asked in: Mathematics - Integrals


1 Verified Answer | Published on 17th 09, 2020

View Answer
Q2 Subjective Hard
Evaluate the integrals:
$$\displaystyle \int \dfrac{1}{\sqrt{4x+3}}dx$$

Asked in: Mathematics - Integrals


1 Verified Answer | Published on 17th 09, 2020

View Answer
Q3 Subjective Medium
Integrate $$\displaystyle \int {\frac{{{v^2}}}{{{v^2} + 2v + 1}}} dx$$

Asked in: Mathematics - Integrals


1 Verified Answer | Published on 17th 09, 2020

View Answer
Q4 Single Correct Medium
$$\displaystyle \int{\dfrac{x^{3}-1}{x^{3}+x}dx}$$ equal to 
  • A. $$x-\log x+\log(x^{2}+1)-\tan^{-1}x+c$$
  • B. $$x+\log x+\dfrac{1}{2}\log(x^{2}+1)+\tan^{-1}x+c$$
  • C. $$x+\log x-\dfrac{1}{2}\log(x^{2}+1)-\tan^{-1}x+c$$
  • D. $$x-\log x+\dfrac{1}{2}\log(x^{2}+1)-\tan^{-1}x+c$$

Asked in: Mathematics - Integrals


1 Verified Answer | Published on 17th 09, 2020

View Answer
Q5 Subjective Medium
$$\int \frac{x}{x^2 + a^2} \;dx$$

Asked in: Mathematics - Integrals


1 Verified Answer | Published on 17th 09, 2020

View Answer