Home
Class 12
MATHS
If int (2)^(e) (1/(logx)-1/(logx)^(2))d...

If ` int _(2)^(e) (1/(logx)-1/(logx)^(2))dx = a + b/(log2) , ` then

A

`a = e,b=-2`

B

` a= e, b=2`

C

`a = -e, b=2`

D

None of these

Text Solution

Verified by Experts

The correct Answer is:
A
Given , `int_(2)^(e)((1)/(logx)-(1)/((logx)^(2)))dx=a+(b)/(log2)`
Put `logx=zrArrx=e^(z)`
`rArrdx=e^(z)dz`
`thereforeint_(2)^(e)e^(z)((1)/(z)+d((1)/(z)))dz=[e^(z)*(1)/(z)]_(log2)^(1)=e-(2)/(log2)`
`thereforea=eandb=-2`
Promotional Banner

Topper's Solved these Questions

  • DEFINITE INTEGRALS

    MHTCET PREVIOUS YEAR PAPERS AND PRACTICE PAPERS|Exercise MHT CET Corner|22 Videos

  • DEFINITE INTEGRALS

    MHTCET PREVIOUS YEAR PAPERS AND PRACTICE PAPERS|Exercise MHT CET Corner|22 Videos

  • CONTINUITY

    MHTCET PREVIOUS YEAR PAPERS AND PRACTICE PAPERS|Exercise MHT CET Corner|16 Videos

  • DIFFERENTIAL EQUATION

    MHTCET PREVIOUS YEAR PAPERS AND PRACTICE PAPERS|Exercise MHT CET Corner|27 Videos

Similar Questions

Explore conceptually related problems

int_(e)^(e^(2)) (1/logx-1/((logx)^(2)))dx=

int(logx)^(2)dx=?

int{(1)/((logx))-(1)/((logx)^(2))}dx=?

int[(1)/(logx)-(1)/((logx)^(2))]dx=

int_(0)^(e^(2)){(1)/((logx))-(1)/((logx)^(2))}dx

int(log(x//e))/((logx)^(2))dx=

int1/(x(1-logx)^(2))dx=

int (log x)/(1+logx)^2 dx

MHTCET PREVIOUS YEAR PAPERS AND PRACTICE PAPERS-DEFINITE INTEGRALS-PRACTICE EXERCISE (Exercise 2) (MISCELLANEOUS PROBLEMS)
  1. The value of int(e^(-1))^(e) (dt)/(t(t+1)) is equal to

    Text Solution

    |

  2. The value of int (1)^(e) 10^(log(e)x) dx is equal to

    Text Solution

    |

  3. If int (2)^(e) (1/(logx)-1/(logx)^(2))dx = a + b/(log2) , then

    Text Solution

    |

  4. int (0)^(oo) (dx)/((x+ sqrt(x^(2)+1))^(3)) is equal to

    Text Solution

    |

  5. The value of the integral int (-pi//2)^(pi//2) sqrt(cos x - cos ^(3) ...

    Text Solution

    |

  6. The value of I=overset(0)underset(-2)int{x^(3)+3x^(2)+3x+3+(x+1)cos(...

    Text Solution

    |

  7. int (alpha)^(beta) sqrt((x-alpha)/(beta -x)) dx is equal to

    Text Solution

    |

  8. Let f(x) be a function satisfyingf'(x)=f(x) withf(0) =1 and g(x) be a ...

    Text Solution

    |

  9. The value overset(2)underset(-2)int {p" In"((1+x)/(1-x))+q" In "((1-...

    Text Solution

    |

  10. Let F (x) = f(x) + f ((1)/(x)), where f (x) = int (1) ^(x ) (log t)/(1...

    Text Solution

    |

  11. If 2f(x) - 3 f(1//x) = x," then " int(1)^(2) f(x) dx is equal to

    Text Solution

    |

  12. int (0)^(2pi) sin^(6) x cos^(5) x dx is equal to

    Text Solution

    |

  13. int (-3pi//2)^(-pi//2) [ ( x + pi)^(3) + cos^(2) x ] dx is equalt to

    Text Solution

    |

  14. int (0)^(3) (3x+1)/(x^(2)+9) dx =

    Text Solution

    |

  15. underset(n to oo)lim underset(r=1)overset(n)sum(1)/(n)e^(r//n) is

    Text Solution

    |

  16. int (-1//2)^(1//2) cos x log ((1+x)/(1-x)) dx = k log 2 , then k equ...

    Text Solution

    |

  17. The value of the integral int (0)^(pi//2) sin ^(5) x dx is

    Text Solution

    |

  18. If int (0)^(x^(2)) f(t) dt = x cos pix , then the value of f(4) is

    Text Solution

    |

  19. If f(x) is differentiable and int0^(t^2)xf(x)dx=2/5t^5, then f(4/(25))...

    Text Solution

    |

  20. The value of int (0)^(pi//2) sin ^(8) x dx is

    Text Solution

    |