Home
Class 12
MATHS
If In=int0^(sqrt(3))(dx)/(1+x^n),(n=1,2,...

If `I_n=int_0^(sqrt(3))(dx)/(1+x^n),(n=1,2,3. .),` then find the value of `("lim")_(n to oo)I_ndot` (a)0 (b) 1 (c) 2 (d) `1/2`

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

If f(n)=int_(0)^(2015)(e^(x))/(1+x^(n))dx , then find the value of lim_(nto oo)f(n)

If I_(n)=int_(0)^((pi)/(4)) tan^(n)x dx , then the value of lim_(n to oo) n(I_(n)+I_(n-2)) is -

Let: a_n=int_0^(pi/2)(1-sint)^nsin2tdt Then find the value of lim_(n->oo)na_n

The value of ("lim")_(n->oo)[(n+1)^2 3-(n-1)^2 3] is_____

int_(0)^(oo)(dx)/([x+sqrt(1+x^(2))]^(n)

("lim")_(ntooo)1/(1+nsin^2n x) is equal to (a) -1 (b) 0 (c) 1 (d) oo

If I_n=int_0^1(dx)/((1+x^2)^n); n in N , then prove that 2nI_(n+1)=2^(-n)+(2n-1)I_n

Find the values of a if f(x)=("lim")_(n rarr oo)(a x^(2n)+2)/(x^(2n)+a+1) is continuous at x=1.

The value of lim_(n to oo) (1^(p)+2^(p)+3^(p)+…+n^(p))/(n^(p+1)) is -

If f(x)={0 ,where x=n/(n+1),n=1,2,3.... and 1 else where then the value of int_0^2 f(x) dx is

CENGAGE PUBLICATION-INTEGRALS-All Questions
  1. The value of int0^pi (sin(n+1/2)x)/(sin (x/2)) dx is, n in I (a) pi/2 ...

    Text Solution

    |

  2. IfI(m , n)=int0^1x^(m-1)(1-x)^(n-1)dx ,(m , n in I ,m ,ngeq0),t h e n...

    Text Solution

    |

  3. If In=int0^(sqrt(3))(dx)/(1+x^n),(n=1,2,3. .), then find the value of ...

    Text Solution

    |

  4. int0^1(tan^(-1)x)/x dx is equals to (a) int0^(pi/2)(sinx)/x dx (b)...

    Text Solution

    |

  5. If int0^1(sint)/(1+t)dt=alpha, then the value of the integral int(4pi-...

    Text Solution

    |

  6. L e tI1=int0^1(e^xdx)/(1+x) a n dI2=int0^1(x^2dx)/(e^(x^3)(2-x^3))dot ...

    Text Solution

    |

  7. int(sintheta)^(costheta)f(xtantheta)dx(w h e r etheta!=(npi)/2,n in I...

    Text Solution

    |

  8. Let g(x)=int0^x f(t).dt,where f is such that 1/2<=f(t)<=1 for t in [0,...

    Text Solution

    |

  9. The value of int0^(pi/2) sin|2x-alpha|dx, where alpha in [0,pi], is (...

    Text Solution

    |

  10. IfIn=int0^pie^x(sin"x")^("n")dx ,t h e n(I3)/(I1)"is equal to" (a) 3/...

    Text Solution

    |

  11. int(-2)^0{(x+1)^3+2+(x+1)cos(x+1)dx is equal to (A) -4 (B) 0 (C) 4 ...

    Text Solution

    |

  12. For any real number x, let [x] denote the largest integer less than or...

    Text Solution

    |

  13. evaluate: int0^(pi/4)2tan^3xdx is

    Text Solution

    |

  14. If f is continuous function and F(x)=int0^x((2t+3)*intt^2f(u)d u)dt , ...

    Text Solution

    |

  15. Let f'(x)=(192x^3)/(2+sin^4pix) for all x in R with f(1/2)=0.If mleint...

    Text Solution

    |

  16. If the value of lim(n rarr oo)(n^(-3/2)) sum(j=1)^(6n) sqrt(j) is equa...

    Text Solution

    |

  17. If int0^xf(t) dt=x+intx^1 tf(t)dt, then the value of f(1)

    Text Solution

    |

  18. If I=int0^((3pi)/4)[(1+x)sinx+(1-x)cosx]dx , then value of (sqrt(2)-1...

    Text Solution

    |

  19. The value of int1^a[x]f^(prime)(x)dx ,where a >1, and [x] denotes the ...

    Text Solution

    |

  20. The value of int(0)^(x)[cost]dt, x epsilon[(4n+1)(pi)/2,(4n+3)(pi)/2] ...

    Text Solution

    |