Home
Class 12
MATHS
lim(lamda to 0)(int(0)^(1) (1+x)^(lambda...

`lim_(lamda to 0)(int_(0)^(1) (1+x)^(lambda ) dx)^(1//lambda)` Is equal to

A

`2 In 2`

B

`(4)/(e)`

C

`In(4)/(e)`

D

4

Text Solution

Verified by Experts

The correct Answer is:
B
Promotional Banner

Topper's Solved these Questions

  • DEFINITE INTEGRAL

    ARIHANT MATHS|Exercise Exercise (More Than One Correct Option Type Questions)|10 Videos

  • DEFINITE INTEGRAL

    ARIHANT MATHS|Exercise Exercise (Passage Based Questions)|17 Videos

  • DEFINITE INTEGRAL

    ARIHANT MATHS|Exercise Exercise For Session 6|10 Videos

  • COORDINATE SYSTEM AND COORDINATES

    ARIHANT MATHS|Exercise Exercise (Questions Asked In Previous 13 Years Exam)|7 Videos

  • DETERMINANTS

    ARIHANT MATHS|Exercise Exercise (Questions Asked In Previous 13 Years Exam)|18 Videos

Similar Questions

Explore conceptually related problems

lim_(lambda rarr0)(int_(0)^(1)(1+x)^(lambda)dx)^((1)/(lambda)) is equal to

int_(0)^(lambda) (ydy)/(sqrt(y+lambda)) is equal to

What is int_(0)^(1) x(1-x)^(n)dx equal to ?

lim_(xto oo) (int_(0)^(x)tan^(-1)dt)/(sqrt(x^(2)+1)) is equal to

What is int_(0)^(1)x (1-x)^(9) dx equal to ?

lim_(x->pi)(2-lambda/x)^(2tan((pipi)/(2lambda)))=1/e, then lambda is equal to -

lim_(x to 0)(int_(0^(x) x e^(t^(2))dt)/(1+x-e^(x)) is equal to

int_(0)^(1)sqrt(x(1-x))dx equals

If int_(0)^(1)cot^(-1)(1-x+x^(2))dx=lambda int_(0)^(1)tan^(-1)xdx, then lambda is equal to 1( b) 2(c)3(d)4

ARIHANT MATHS-DEFINITE INTEGRAL-Exercise (Single Option Correct Type Questions)
  1. For f(x) =x^(4) +|x|, let I(1)= int (0)^(pi)f(cos x) dx and I(2)= int(...

    Text Solution

    |

  2. Let f be a positive function. If I1 = int(1-k)^k x f[x(1-x)]\ dx and I...

    Text Solution

    |

  3. Suppose that the quadratic function f(x) = ax^(2) + bx +c is non-negat...

    Text Solution

    |

  4. Let I (a) =int(0)^(pi) ((x)/(a)+ a sin x)^(2) dx, where 'a' is positiv...

    Text Solution

    |

  5. The set of value of 'a' which satisfy the equation int0^2(t-log2a)dt...

    Text Solution

    |

  6. lim(x rarr infty) (x^(3) int(-1//x)^(1//x)("In" (1+t^(2)))/(1+e^(t)) d...

    Text Solution

    |

  7. The value of sqrt(pi(int(0)^(2008)x| sinpi x| dx)) is equal to

    Text Solution

    |

  8. lim(n rarr infty) sum(k=1)^(n) (n)/(n^(2)+k^(2)x^(2)),x gt 0 is equa...

    Text Solution

    |

  9. Let a gt 0 and f(x) is monotonic increase such that f(0)=0 and f(a)=b...

    Text Solution

    |

  10. int(-1/sqrt3)^(-1/sqrt3)(x^4)/(1-x^4)cos^(- 1)((2x)/(1+x^2))dx

    Text Solution

    |

  11. int(0)^(infty)f(x+(1)/(x)). (In x )/(x)dx is equal to

    Text Solution

    |

  12. lim(lamda to 0)(int(0)^(1) (1+x)^(lambda ) dx)^(1//lambda) Is equal t...

    Text Solution

    |

  13. If g(x) is the inverse of f(x) and f(x) has domain x in [1,5], where...

    Text Solution

    |

  14. The value of the definite integral int(0)^(pi//2)sin x sin 2x sin 3x d...

    Text Solution

    |

  15. If f(x)= int(0)^(x)(f(t))^(2) dt, f:R rarr R be differentiable functi...

    Text Solution

    |

  16. The number of integral solutions of the equation 4int (0)^( infty)(In"...

    Text Solution

    |

  17. int(0)^(16n^(2)//pi) "cos" (pi)/(2)[(xpi)/(n)] dx is equal to

    Text Solution

    |

  18. If int-2^-1 (ax^2-5)dx=0 and 5 + int1^2 (bx + c) dx = 0, then

    Text Solution

    |

  19. The value of int(3)^(6)(sqrt(x+sqrt(12x-36))+sqrt(x-sqrt(12x- 36)))dx...

    Text Solution

    |

  20. Let In=int(-n)^n({x+1}*{x^2+2}+{x^2+2}{x^3+4})dx, where {*} denotet th...

    Text Solution

    |