Home
Class 12
MATHS
int(-pi/3)^0[cot^(-1)(2/(2cosx-1))+cot^(...

`int_(-pi/3)^0[cot^(-1)(2/(2cosx-1))+cot^(-1)(cosx-1/2)]dxi se q u a lto` `(pi^2)/6` (b) `(pi^2)/3` (c) `(pi^2)/8` (d) `(3pi^2)/8`

A

`(pi^(2))/6`

B

`(pi^(2))/3`

C

`(pi^(2))/8`

D

`(3pi^(2))/8`

Text Solution

Verified by Experts

The correct Answer is:
A
For `x epsilon(-(pi)/3,0),2 cos x-1gt0`
`:.I=int_(-pi//3)^(pi)//2 dx=(pi^(2))/6`
Promotional Banner

Topper's Solved these Questions

  • DEFINITE INTEGRATION

    CENGAGE PUBLICATION|Exercise MCQ_TYPE|27 Videos

  • DEFINITE INTEGRATION

    CENGAGE PUBLICATION|Exercise LC_TYPE|31 Videos

  • DEFINITE INTEGRATION

    CENGAGE PUBLICATION|Exercise CAE_TYPE|88 Videos

  • CURVE TRACING

    CENGAGE PUBLICATION|Exercise EXERCISES|24 Videos

  • DETERMINANT

    CENGAGE PUBLICATION|Exercise Multiple Correct Answer|5 Videos

Similar Questions

Explore conceptually related problems

int_(-pi/3)^0[cot^(-1)(2/(2cosx-1))+cot^(-1)(cosx-1/2)]dx i s equal to (pi^2)/6 (b) (pi^2)/3 (c) (pi^2)/8 (d) (3pi^2)/8

int_0^pi(xtanx)/(secx+cosx)dx is (pi^2)/4 (b) (pi^2)/2 (c) (3pi^2)/2 (d) (pi^2)/3

3 cot ^(-1)""(1)/(2-sqrt(3))+cot ^(-1)""x=(pi)/(2)

int_(0)^((pi)/(2))(dx)/(1+cosx)

int_(0)^(pi)(dx)/(3+2sinx+cosx)

int_(-(pi)/(2))^((pi)/(2))(dx)/(1+cot^(4)x)

int_(0)^((pi)/(2))(xdx)/(1+cosx)

cos^(-1)("cos"(2cot^(-1)(sqrt(2)-1))) is equal to (a) sqrt(2)-1 (b) pi/4 (c) (3pi)/4 (d) none of these

cot ^(-1)""x+cot^(-1)""2x=(3pi)/(4)

cot ^(-1) ""(1)/(2) -(1)/(2) cot^(-1)"" (4)/(3) =(pi)/(4)

CENGAGE PUBLICATION-DEFINITE INTEGRATION -SCQ_TYPE
  1. The numbers of possible continuous f(x) defined in [0,1] for which I1...

    Text Solution

    |

  2. Suppose that F(x) is an anti-derivative of f(x)=(sinx)/x ,w h e r ex >...

    Text Solution

    |

  3. int(-pi/3)^0[cot^(-1)(2/(2cosx-1))+cot^(-1)(cosx-1/2)]dxi se q u a lto...

    Text Solution

    |

  4. Evaluate the definite integrals int(0)^(pi//4)(sinx+cosx)/(25-16(...

    Text Solution

    |

  5. int- 1^1(e^(-1/ x))/(x^2(1+e^(-2/ x)))dx is equal to :

    Text Solution

    |

  6. If int0^oosinx/xdx=pi/2, then int0^oosin^3x/xdx is equal to

    Text Solution

    |

  7. The range of the function f(x)=int(-1)^(1)(sinxdt)/(1-2tcosx+t^(2)) is

    Text Solution

    |

  8. If the function f : [0,8] to R is differentiable, then for 0 < alpha...

    Text Solution

    |

  9. If f(x)=x^(5)+5x-1 then int(5)^(41)(dx)/((f^(-1)(x))^(5)+5f^(-1)(x)) e...

    Text Solution

    |

  10. Let f(0)=0a n dint0^2f^(prime)(2t)e^(f(2t))dt=5.t h e nv a l u eoff(4)...

    Text Solution

    |

  11. If f(x)="cos"(tan^(-1)x), then the value of the integral int0^1xf''(x)...

    Text Solution

    |

  12. The equation of the curve is y=f(x)dot The tangents at [1,f(1),[2,f(2)...

    Text Solution

    |

  13. The value of int1^e((tan^(-1)x)/x+(logx)/(1+x^2))dx ,is (a) tane (b)...

    Text Solution

    |

  14. If f(pi) = 2 and int0^pi (f(x)+f^('')(x)) sinx dx=5, then f(0) is equa...

    Text Solution

    |

  15. If int1^2e^x^2dx=a ,t h e ninte^(e^4)sqrt(1n x)dxi se q u a lto 2e^4-...

    Text Solution

    |

  16. If f(x) is continuous for all real values of x , then sum(r=1)^nf(r-1...

    Text Solution

    |

  17. T h ev a l u eofint0^(pi/2)sin|2x-alpha|dx ,w h e r ealpha in [0,pi],i...

    Text Solution

    |

  18. f(x) is a continuous function for all real values of x and satisfies i...

    Text Solution

    |

  19. If f(x)=int(-1)^(x)|t|dt, then for any xge0,f(x) equals

    Text Solution

    |

  20. The value of int(-a)^a(cos^(- 1)x-sin^(- 1)sqrt(1-x^2))dx is (a>0) w...

    Text Solution

    |