Home
Class 12
MATHS
If In = int0^(pi//4) tan^n x dx, then li...

If `I_n = int_0^(pi//4) tan^n x dx`, then `lim_(n to oo) n [I_n + I_(n -2)]` equals :

A

44228

B

1

C

`oo`

D

zero

Text Solution

Verified by Experts

The correct Answer is:
B
Promotional Banner

Topper's Solved these Questions

  • COORDINATE SYSTEMS, LOCUS AND STRAIGHT LINES

    HIMALAYA PUBLICATION|Exercise QUESTION BANK|297 Videos

  • DIFFERENTIAL EQUATIONS

    HIMALAYA PUBLICATION|Exercise QUESTION BANK|206 Videos

Similar Questions

Explore conceptually related problems

If U_(n) = int_0^(pi/4) tan^(n) x dx then u_(n)+u_(n-2) =

If I_(n) = int_0^(pi/4) tan^(n)x dx , then n(I_(n-1)+I_(n+1)) =

I_(n) = int_0^(pi/4) tan^(n) x dx, n in N , then I_(10)+I_(8) =

If I_(n) = int_0^(pi/2) sin^(n)x dx then I_(n)/(I_(n-2)) =

If I_(n) = int_0^(pi/4) tan^(n) theta d theta , then I_(8)+I_(6) equals

If I_n = int_0^(pi//4) tan^n theta d theta , then for any +ve integer n, the value of n(I_(n - 1) + I_(n + 1)) is :

If n(ne 1) in N and I_(n) = int tan^(n) x dx then I_(n)+I_(n-2) =

If n in N and I_(n) = int (log x)^(n) dx , then I_(n) + n I_(n - 1) =

HIMALAYA PUBLICATION-Definite Integrals and its Application-QUESTION BANK
  1. int0^(10pi) |sin x| dx is

    Text Solution

    |

  2. int(-pi)^(pi) (2x(1 + sin x))/(1 + cos^2 x) dx is :

    Text Solution

    |

  3. If In = int0^(pi//4) tan^n x dx, then lim(n to oo) n [In + I(n -2)] eq...

    Text Solution

    |

  4. If f(a + b - x) = fx, then inta^b x f(x) dx is equal to :

    Text Solution

    |

  5. The value of the integral I = int0^1 x (1 - x)^(n) dx is :

    Text Solution

    |

  6. Let d/(dx) F(x) = ((e^(sin x))/(x)) , x > 0. If int1^4 3/x e^(sin x^3)...

    Text Solution

    |

  7. If f(y) = e^(y), g(y) = y , y > 0 and F(t) = int0^t f(t - y) g(y) dy...

    Text Solution

    |

  8. Let f(x) be a function satisfying f'(x) = f(x) with f(0) = 1 and g(x) ...

    Text Solution

    |

  9. If f(x) = (e^x)/(1 + e^x) , I1 = int(f(-a))^(f(a)) x g {x(1 - x)} dx a...

    Text Solution

    |

  10. The value of I = int0^(pi//2) ((sin x + cos x)^2)/(sqrt(1 + sin 2x)) d...

    Text Solution

    |

  11. The value of int(-2)^3 |1 - x^2| dx is:

    Text Solution

    |

  12. If int0^pi x f (sin x)dx = A int0^(pi//2) f (sin x) dx, then A is :

    Text Solution

    |

  13. Let F : R to R be a differentiable function having : f(2) = 6, f'(2) =...

    Text Solution

    |

  14. int0^(pi) x f (sin x) dx is equal to :

    Text Solution

    |

  15. int(-3pi//2)^(-pi//2) [(x +pi)^3 + cos^2 (x + 3x)]dx is equal to :

    Text Solution

    |

  16. If f(x) ={(e^(cosx)sinx; |x| le 2),(2 ; othe...

    Text Solution

    |

  17. The value of integral int(e^(-1))^(e^2) |(loge x)/(x)| dx is :

    Text Solution

    |

  18. Let g(x) = int0^(x) f(t) dt, where 1/2 le f(t) < 1, t in [0,1] and 0 <...

    Text Solution

    |

  19. The value of int(-pi)^(pi) (cos^2 x)/(1 + a^x) dx, a > 0, is :

    Text Solution

    |

  20. Let f : (0, oo ) to R and F(x) = int0^x f(t) dt. If F(x^2) = x^2(1 +...

    Text Solution

    |