Home
Class 12
MATHS
int0^1log(sqrt(1-x)+sqrt(1+x))dx equals:...

`int_0^1log(sqrt(1-x)+sqrt(1+x))dx` equals:

A

`(1)/(2) ( log 2 - (1)/(2) + (pi)/(4) )`

B

`(1)/(2) ( log 2 -1 + (pi)/(2))`

C

`(1)/(3)( log 4 -1 + (pi)/(8) )`

D

`(1)/(4) (log 3-1 + (pi)/(2))`.

Text Solution

Verified by Experts

The correct Answer is:
B
Promotional Banner

Topper's Solved these Questions

  • DEFINITE INTEGRALS

    MCGROW HILL PUBLICATION|Exercise EXERCISE (LEVEL 2) Numerical Answer Type Questions|19 Videos

  • DEFINITE INTEGRALS

    MCGROW HILL PUBLICATION|Exercise Questions from Previous Years. AIEEE/ JEE Main Papers|65 Videos

  • DEFINITE INTEGRALS

    MCGROW HILL PUBLICATION|Exercise EXERCISE (LEVEL 1) Single Correct Answer Type Questions|43 Videos

  • COMPLEX NUMBERS

    MCGROW HILL PUBLICATION|Exercise QUESTIONS FROM PREVIOUS YEARS. B-ARCHITECTURE ENTRANCE EXAMINATION PAPER|17 Videos

  • DETERMINANTS

    MCGROW HILL PUBLICATION|Exercise QUESTIONS FROM PREVIOUS YEARS B-ARCHITECTURE ENTRANCE EXAMINATION PAPERS|18 Videos

Similar Questions

Explore conceptually related problems

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

The value of int log(sqrt(1-x)+sqrt(1+x))dx, is equal to

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

int_0^1 1/(sqrt(x+3)-sqrt(x+1)) dx

int ln(sqrt(1+x)+sqrt(1-x))dx

int_(0)^(1)(1)/(sqrt(1+x)-sqrt(x))dx

Find int_-1^1 ln(sqrt(1-x)+sqrt(1+x))dx

int_0^1 x/sqrt(1+x)dx

int_0^1 x/sqrt(1-x^2)dx

MCGROW HILL PUBLICATION-DEFINITE INTEGRALS-EXERCISE (LEVEL 2) Single Correct Answer Type Questions
  1. Let f be a continuous function on R satisfying f(x+y)= f(x) + f(y) for...

    Text Solution

    |

  2. If f(x) = cosec (x-pi/3) cosec (x-pi/6), then the value of int0^(pi/2)...

    Text Solution

    |

  3. int0^1log(sqrt(1-x)+sqrt(1+x))dx equals:

    Text Solution

    |

  4. If l=int(0)^(1//2)(dx)/(sqrt(1-x^(2n))), n in N then (Where, [.] den...

    Text Solution

    |

  5. The numbers A, B and C such that a function of the form f(x) = Ax^(2) ...

    Text Solution

    |

  6. The equation of the tangent to the curve y=int(x)^(x^2) log t dt at x=...

    Text Solution

    |

  7. The value of int(- pi//2)^(pi//2) ((2- sin theta)/( 2+ sin theta)) d t...

    Text Solution

    |

  8. The value of the integral overset(pi//4)underset(0)int (sinx+cosx)/(3+...

    Text Solution

    |

  9. If I1=intx^1 1/(1+t^2)dt and I2=int1^(1/x) 1/(1+t^2)dt for xgt0 then (...

    Text Solution

    |

  10. The solution for x of the equation overset(x)underset(sqrt(2))int(1)...

    Text Solution

    |

  11. The mean value of the function f(x)= 2/(e^x+1) in the interval [0,2] i...

    Text Solution

    |

  12. int(0)^(pi) x log sinx dx

    Text Solution

    |

  13. overset(pi)underset(-ip)int [cos px-sin qx]^(2) dx where p,q are integ...

    Text Solution

    |

  14. Let f,g and h be continuous functions on [0,a] such that f(x) = f(a-x)...

    Text Solution

    |

  15. Ifint(pi/3)^xsqrt((3-sin^2t))dt+int0^ycostdt=0,t h e ne v a l u a t e(...

    Text Solution

    |

  16. If P(x) is a polynomial of the least degree that has a maximum equal ...

    Text Solution

    |

  17. Let P(x) be a polynomial of least degree whose graph has three points ...

    Text Solution

    |

  18. lim(n->oo){(e^(1//n))/(n^2)+(2*(e^(1//n))^2)/(n^2)+(3*(e^(1//n))^3)/(n...

    Text Solution

    |

  19. The value of int0^1lim(n->oo)sum(k=0)^n(x^(k+2)2^k)/(k!)dx is:

    Text Solution

    |

  20. The value of int(0)^(1) (x^( 2 alpha) - 1)/( log x) dx, if alpha = (2n...

    Text Solution

    |