Home
Class 12
MATHS
Prove that int0^oo[n e^(-x)]dx=ln((n^n...

Prove that `int_0^oo[n e^(-x)]dx=ln((n^n)/(n !)),w h e r en` is a natural number greater than 1 and [.] denotes the greatest integer function..

Promotional Banner

Topper's Solved these Questions

  • INEQUALITIES INVOLVING MEANS

    CENGAGE PUBLICATION|Exercise Jee Advanced (Single|1 Videos

  • INTRODUCTION TO VECTORS

    CENGAGE PUBLICATION|Exercise TRUE OR FALSE|1 Videos

Similar Questions

Explore conceptually related problems

Evaluate: int_0^2[x^2-x+1]dx ,w h e r e[dot] denotos the greatest integer function.

Prove that: I_n=int_0^oox^(2n+1) e^ (-x^2) dx=(n !)/2,n in N .

Evaluate: int_(-5)^5x^2[x+1/2]dx(w h e r e[dot] denotes the greatest integer function).

Evaluate: int_1^(e^6)[(logx)/3]dx ,w h e r e[dot] denotes the greatest integer function.

The value of int_0^1.5 [x^2] dx is : where [x] denotes greatest integer function.

Evaluate lim_(n->oo) [sum_(r=1)^n1/2^r] , where [.] denotes the greatest integer function.

Let n be an odd natural number greater than 1. Then , find the number of zeros at the end of the sum 99^n+1.

Evaluate: int_0^oo[2e^(-x)]dx ,w h e r e[x] represents greatest integer function.

The integral int_0^(1. 5)[x^2]dx ,w h e r e[dot] denotoes the greatest integer function, equals ...........

Find the value of : int_0^(10)e^(2x-[2x])d(x-[x])w h e r e[dot] denotes the greatest integer function).

CENGAGE PUBLICATION-INTEGRALS-All Questions
  1. Prove that int0^1xe^xdx=1

    Text Solution

    |

  2. I1=int0^(pi/2)ln(sinx)dx ,I2=int(-pi/4)^(pi/4)ln(sinx+cosx)dxdot Then ...

    Text Solution

    |

  3. Prove that int0^oo[n e^(-x)]dx=ln((n^n)/(n !)),w h e r en is a na...

    Text Solution

    |

  4. For x in R and a continuous function f, let I1=int(sin^2t)^(1+cos^2t)...

    Text Solution

    |

  5. Evaluate of each of the following integrals int(pi//6)^(pi//3)(sqrt...

    Text Solution

    |

  6. Given a function f:[0,4]toR is differentiable ,then prove that for som...

    Text Solution

    |

  7. Evaluate: int0^(pi/2)log((4+3sinx)/(4+3cosx))dx

    Text Solution

    |

  8. The value of int0^1 4x^3 {d^2/(dx^2) (1 - x^2)^5 } dx is

    Text Solution

    |

  9. Evaluate: int(-pi)^(3pi)log(s e c theta-t a ntheta)d theta

    Text Solution

    |

  10. The value of the integral overset(1)underset(0)int e^(x^(2))dx lies in...

    Text Solution

    |

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

    Text Solution

    |

  12. If In=int0^1(dx)/((1+x^2)^n); n in N , then prove that 2nI(n+1)=2^(-n...

    Text Solution

    |

  13. If f(0)=1,f(2)=3,f^'(2)=5,then find the value of int0^1xf^('')(2x)d...

    Text Solution

    |

  14. Ifinta^b(f(x))/(f(x)+f(a+b-x))dx=10 ,t h e n (a) b=22 ,a=2 (b) b=15 ...

    Text Solution

    |

  15. Evaluate: int0^pi(dx)/(1+sinx)

    Text Solution

    |

  16. if In=int0^(pi/4)tan^ntheta.d theta,then n in N,n(I(n-1)+I(n+1)) equal...

    Text Solution

    |

  17. Consider the integral int0^(2pi)(dx)/(5-2cosx) making the substitutio...

    Text Solution

    |

  18. If f(x)=int0^x |t-1| dt, where 0 lt= x lt= 2 then (a) range of f(x) ...

    Text Solution

    |

  19. If int0^1(e^(-x)dx)/(1+e^x)=(log)e(1+e)+k , then find the value of k.

    Text Solution

    |

  20. The value of int0^oo (dx)/(1+x^4) is

    Text Solution

    |