Home
Class 12
MATHS
int(-1)^(1)log(x+sqrt(x^(2)+1)) dx is eq...

` int_(-1)^(1)log(x+sqrt(x^(2)+1))` dx is equal to

A

0

B

log 2

C

`log. 1/2`

D

None of these

Text Solution

Verified by Experts

The correct Answer is:
A
Let f(x) = log `(x+sqrt(1+x^(2)))`and replacing x by -x , we get
` f(-x) = log (sqrt(1+x^(2))-x)`
` = log [ (sqrt(1+x^(2))-x) ((sqrt(1+x^(2))+x))/((sqrt(1+x^(2))+x))]`
` = log. ([ (1+x^(2))-x^(2)])/((sqrt(1+x^(2))+x))= log 1 - log (sqrt(1+x^(2))+x)`
` = - log (sqrt(1+x^(2))+x)=f(x)`
Hence, f(x) is an odd function .
` :. int _(-1)^(1) log (x+sqrt(1+x^(2)))dx = 0 `
Promotional Banner

Topper's Solved these Questions

  • DEFINITE INTEGRALS

    MHTCET PREVIOUS YEAR PAPERS AND PRACTICE PAPERS|Exercise PRACTICE EXERCISE (Exercise 2) (MISCELLANEOUS PROBLEMS)|76 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

The value of the integral int_(-1)^(1)log(x+sqrt(x^(2)+1))dx is

int_(-a)^(a) log (x+ sqrt(x^(2) + 1 ) ) dx

int_(0)^(1)(log x)/(sqrt(1-x^(2)))dx

The value of the integral int_(-1)^(1)log_(e)(sqrt(1-x)+sqrt(1+x))dx is equal to :

int_(1)^(x) (log(x^(2)))/(x) dx is equal to

int_(0)^(1)log(sqrt(1-x)+sqrt(1+x))dx equals:

The value of definite integral int_(1/3)^(2/3)(ln x)/(ln(x-x^(2)))dx is equal to :

int_(1)^(2)x^(2x^(2)+1)(1+2ln x)dx is equal to

MHTCET PREVIOUS YEAR PAPERS AND PRACTICE PAPERS-DEFINITE INTEGRALS-MHT CET Corner
  1. int(-1)^(1)log(x+sqrt(x^(2)+1)) dx is equal to

    Text Solution

    |

  2. int (-pi/2)^(pi/2)log((2-sin x)/(2+sinx))dx is equal to

    Text Solution

    |

  3. int (0)^(pi //2)((root(n)(secx))/(root(n)(secx)+root(n)("cosec"x)))dx=

    Text Solution

    |

  4. The value of int 0 ^ 1 x ^ 2 ( 1 - x ^ 2 ) ^ (3//2 ) dx ...

    Text Solution

    |

  5. The value of int0^oox/((1+x)(x^2+1))dx is

    Text Solution

    |

  6. Evaluate int(0)^(pi)(x dx)/(1+cos alpha sin x),where 0lt alpha lt pi.

    Text Solution

    |

  7. int(pi//2)^(pi//2)(cosx)/(1+e^(x))dx is equal to

    Text Solution

    |

  8. int(0)^(pi//2)(1)/((1+tanx))dx=?

    Text Solution

    |

  9. If int(0)^(1) tan^(-1) x dx = p , then the value of int(0)^(1) tan^(-1...

    Text Solution

    |

  10. The value of int (0)^(pi//2) log ("cosec "x) dx is

    Text Solution

    |

  11. Which of the following is true ?

    Text Solution

    |

  12. int(0)^(5) 1/((x-1)(x-2))dx is equal to

    Text Solution

    |

  13. int(pi/4)^(pi/2) e^x(logsinx+cotx)dx

    Text Solution

    |

  14. The value of int(0)^(pi) x sin^(3) x dx is

    Text Solution

    |

  15. The value of int0 ^(pi/2) (cos3x+1)/(cosx - 1) dx is equal to

    Text Solution

    |

  16. The value of underset(0)overset(1)int tan^(-1) ((2x-1)/(1+x-x^(2)))dx ...

    Text Solution

    |

  17. If f is a continous function, then

    Text Solution

    |

  18. The value of int(-pi)^(pi) sin^(3) x cos^(2) x dx is equal to

    Text Solution

    |

  19. The value of int(-1)^(1) log ((x-1)/(x+1))dx is

    Text Solution

    |

  20. int(pi//6)^(pi//3)(1)/((1+sqrt(tanx)))dx=(pi)/(12)

    Text Solution

    |

  21. int (1)^(2)e^(x) (1/x - 1/(x^(2)))dx is qual to

    Text Solution

    |