Mathematics

The value of the integral $$\displaystyle \int _{ { e }^{ -1 } }^{ { e }^{ 2 } }{ \left| \frac { \log _{ e }{ x }  }{ x }  \right| dx } $$ is


ANSWER

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


View Full Answer

Its FREE, you're just one step away


Single Correct Medium Published on 17th 09, 2020
Next Question
Questions 203525
Subjects 9
Chapters 126
Enrolled Students 86
Enroll Now For FREE

Realted Questions

Q1 Single Correct Medium
Using integral $$\int _{ 0 }^{ \pi /2 }{ \ln { \left( \sin { x }  \right)  }  } dx=\int _{ 0 }^{ \pi /2 }{ \ln { \left( \sec { x }  \right)  }  } dx=-\cfrac { \pi  }{ 2 } \ln { 2 } $$
Evaluate $$\int _{ -\pi /4 }^{ \pi /4 }{ \ln { \left( \cfrac { \sin { x } +\cos { x }  }{ \cos { x } -\sin { x }  }  \right)  } dx= } $$
  • A. $$\pi \ln{2}$$
  • B. $$\cfrac{\pi \ln{2}}{2}$$
  • C. $$-\pi \ln{2}$$
  • D. $$0$$

Asked in: Mathematics - Integrals


1 Verified Answer | Published on 17th 09, 2020

View Answer
Q2 Subjective Medium
The value of integral $$\displaystyle\int^{\pi /2}_{\pi_{/4}}{\cos x}dx$$ is?

Asked in: Mathematics - Integrals


1 Verified Answer | Published on 17th 09, 2020

View Answer
Q3 Subjective Hard
Evaluate: $$\displaystyle\int_{0}^{\dfrac{\pi}{2}}\sqrt{sin\,\phi} \, cos^5\,\phi\,d\,\phi$$

Asked in: Mathematics - Integrals


1 Verified Answer | Published on 17th 09, 2020

View Answer
Q4 Single Correct Medium
If $$\int { \cfrac { \left( { x }^{ 2 }+1 \right) \left( { x }^{ 2 }+4 \right)  }{ \left( { x }^{ 2 }+3 \right) \left( { x }^{ 2 }-5 \right)  }  } dx=\int { \left\{ 1+\cfrac { f(x) }{ \left( { x }^{ 2 }+3 \right) \left( { x }^{ 2 }-5 \right)  }  \right\}  } dx$$
$$x+A\tan ^{ -1 }{ \left( \cfrac { x }{ A' }  \right)  } +B\log { \left( \cfrac { x-l }{ x+m }  \right)  } +K\quad $$ then which of the following is correct
  • A. $$A=\cfrac { 1 }{ 4\sqrt { 3 } } ,B=\cfrac { 27 }{ 8\sqrt { 5 } } ,K\in R$$
  • B. $$f(x)=7{ x }^{ 2 }+19,A'=\sqrt { 3 } ,K\in R$$
  • C. $$l=m=\sqrt { 5 } ,L=1,K\in R$$
  • D. All of these

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