Home
Class 12
MATHS
If [x] denote the greatest integer funct...

If [x] denote the greatest integer function , then , `int_(0)^(pi//6) (1 - cos 2x)/(1 + cos 2x) d(x - [x]) = `

A

`1/sqrt3 +pi/6`

B

`1/sqrt3 - pi/6`

C

`sqrt3 - pi/6`

D

`sqrt3 + pi/6`

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

int_(0)^(pi//2) cos 2x dx .

Evaluate : int_(0)^(pi//2) ( sin x)/(1 +cos ^2 x) dx

int_0^(pi//4) (sin x + cos x)/(3 + sin 2x ) dx =

If [x] denotes the greatest integer function, then : ""_(2)^(4)([x] - 1)([x] -2)([x] - 3)([x] - 4)dx =

int_(0)^(pi//2) (sin x)/(1 +cos^2) dx .

int (cos 2x-1)/(cos 2x+1) dx =

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

If [x] is the greatest integer function not greater than x , then int_(0)^(11) [x] dx =

Let [cdot] denote the greatest integer function, then the value of int_(0)^(1.5)x [x^2] dx is :

HIMALAYA PUBLICATION-Definite Integrals and its Application-QUESTION BANK
  1. int(1)^(3)(x-1)(x-2)(x-3)dx=

    Text Solution

    |

  2. If 2f(x)- 3f(1/x) = x then int1^(e) f(x) dx =

    Text Solution

    |

  3. If [x] denote the greatest integer function , then , int(0)^(pi//6) (1...

    Text Solution

    |

  4. The value of the integral, int3^6 (sqrt(x))/(sqrt(9 - x) + sqrt(x))dx ...

    Text Solution

    |

  5. int0^(10pi) |sin x| dx is

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |