Home
Class 12
MATHS
The value of underset(n rarroo)(lim)sum(...

The value of `underset(n rarroo)(lim)sum_(r=1)^(n)(1)/(sin{((n+r)pi)/(4n)}).(pi)/(n) ` is equal to

A

`2ln(sqrt(2)-1)`

B

`4ln(sqrt(2)-1)`

C

`4ln(sqrt(2)+1)`

D

`lnsqrt(2)`

Text Solution

Verified by Experts

Promotional Banner

Topper's Solved these Questions

  • DEFINITE INTEGRAL

    FIITJEE|Exercise ASSIGNMENT PROBLEMS (OBJECTIVE) (LEVEL-II)|15 Videos

  • DEFINITE INTEGRAL

    FIITJEE|Exercise COMPREHENSION I:|3 Videos

  • DEFINITE INTEGRAL

    FIITJEE|Exercise ASSIGNMENT PROBLEMS (SUBJECTIVE) (LEVEL-II)|10 Videos

  • COMPLEX NUMBER

    FIITJEE|Exercise NUMERICAL BASED|3 Videos

  • DETERMINANT

    FIITJEE|Exercise NUMERICAL BASED|3 Videos

Similar Questions

Explore conceptually related problems

The value of lim_(n rarroo) sum_(r=1)^(n)(1)/(sin{((n+r)pi)/(4n)}).(pi)/(n) is equal to

sum_(n=1)^(oo)((1)/(4n-3)-(1)/(4n-1))=(pi)/(n) find n

The value of lim_(n rarr oo)(1)/(n)sum_(r=1)^(n)((r)/(n+r)) is equal to

The value of lim_(n rarr oo)sum_(r=1)^(n)(sum_(t=0)^(r-1)(1)/(5^(n))*C(n,r)C(r,t)3^(t)) is equal to

The value of lim_(n rarr oo)sum_(i=1)^(n)(i)/(n^2)sin((pi i^(2))/(n^(2))) is equal to

"lim_(n rarr oo)(1)/(n){sum_(r=1)^(n)e^((r)/(n))}=

Find the value of lim_(n rarr oo)sum_(r=1)^(n)(r^(2))/(n^(3)+n^(2)+r)

FIITJEE-DEFINITE INTEGRAL -ASSIGNMENT PROBLEMS (OBJECTIVE) (LEVEL-I)
  1. The value of int(0)^(1)(Pi(i=1)^(n)(x+i))(Sigma(j=1)^(n)(1)/(x+j))dx i...

    Text Solution

    |

  2. The value of underset(n rarroo)(lim)sum(r=1)^(n)(1)/(sin{((n+r)pi)/(4n...

    Text Solution

    |

  3. if f(x)=|[x,cosx,e^(x^2)],[sinx,x^2,secx],[tanx,1,2]| then the value o...

    Text Solution

    |

  4. The value of integral underset(a)overset(b)int(|x|)/(x)dx, a lt b is :

    Text Solution

    |

  5. If int(0)^(1)(ax+b)/(x^(2)+3x+2)dx=ln.(3)/(2), then

    Text Solution

    |

  6. If f(0)=2,f'(x)=f(x),phi(x)=x+f(x)" then "int(0)^(1)f(x)phi(x)dx is

    Text Solution

    |

  7. Let f(x) be a function satisfyingf'(x)=f(x) withf(0) =1 and g(x) be a ...

    Text Solution

    |

  8. int(0)^(alpha)(1)/(cosx+cosalpha)dx is equal to

    Text Solution

    |

  9. If int(-pi//4)^(3pi//4)(e^(pi//4)dx)/((e^(x)+e^(pi//4))(sinx+cosx))=ki...

    Text Solution

    |

  10. The value of int(0)^(2pi)|cosx-sinx|dx is equal to

    Text Solution

    |

  11. int(0)^(pi//2)(dx)/(1+e^(sqrt(2)cos(x+(pi)/(4)))) is equal to

    Text Solution

    |

  12. int(0)^(pi//2n)(dx)/(1+(cotnx)^(n)) is equal to (ninN)

    Text Solution

    |

  13. The value of int(0)^(4pi)|sinx|-[(|sinx|)/(2)]-[(|cosx|)/(2)]dx is

    Text Solution

    |

  14. If f((1)/(x))+x^(2)f(x)=0,AAxgt0 then int(sinx)^(cosecx)f(z)dz is for ...

    Text Solution

    |

  15. The value of the integral int(pi//6)^(pi//3)(dx)/(1+tan^(5)x) is

    Text Solution

    |

  16. For any integer n, the integral int0^pie^(cosx)cos^3(2n+1)xdx has the ...

    Text Solution

    |

  17. The value of int(0)^(pi//2)ln((sin^(2)theta)/(cos^(3)theta))d theta is

    Text Solution

    |

  18. int(-1)^(1)[tan^(-1){sin(cos^(-1)x)}+cot^(-1){cos(sin^(-1)x)}dx=

    Text Solution

    |

  19. int- 8^8(sin^(93)x+x^(295))\ dx

    Text Solution

    |

  20. Let I=int0^1(sin)/(sqrt(x))dx"and"J=int0^1(cosx)/(sqrt(x))dx Then w...

    Text Solution

    |