Home
Class 12
MATHS
Evaluate int (0)^(pi//2)ln((1+a sin x)/(...

Evaluate `int _(0)^(pi//2)ln((1+a sin x)/(1- a sin x)) (dx)/(sinx) (|a|lt1)`

Text Solution

Verified by Experts

The correct Answer is:
`=pi^(-1) a +C`
Promotional Banner

Topper's Solved these Questions

  • DEFINITE INTEGRAL

    ARIHANT MATHS|Exercise Exercise For Session 1|15 Videos

  • DEFINITE INTEGRAL

    ARIHANT MATHS|Exercise Exercise For Session 2|14 Videos

  • COORDINATE SYSTEM AND COORDINATES

    ARIHANT MATHS|Exercise Exercise (Questions Asked In Previous 13 Years Exam)|7 Videos

  • DETERMINANTS

    ARIHANT MATHS|Exercise Exercise (Questions Asked In Previous 13 Years Exam)|18 Videos

Similar Questions

Explore conceptually related problems

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

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

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

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

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

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

int_(0)^(pi/2) sin^(-1)(sin x)dx

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

int_(0)^(pi)(x sin x)/(1-sin x)dx=

Evaluate int_(0)^(pi)(sin 6x)/(sinx) dx .

ARIHANT MATHS-DEFINITE INTEGRAL-Exercise (Questions Asked In Previous 13 Years Exam)
  1. Evaluate int (0)^(pi//2)ln((1+a sin x)/(1- a sin x)) (dx)/(sinx) (|a|l...

    Text Solution

    |

  2. The value of int(-pi//2)^(pi//2) (x^(2)cos x )/(1+e^(x)) dx is equal ...

    Text Solution

    |

  3. The total number for distinct x epsilon[0,1] for which int(0)^(x)(t^(2...

    Text Solution

    |

  4. Let f(x)=7 tan^(8) x +7 tan^(6) x-3 tan^(4) x-3 tan^(2)x for all x in...

    Text Solution

    |

  5. Let f prime(x)=(192x^3)/(2+sin^4 pix) for all x in RR with f(1/2)=0. I...

    Text Solution

    |

  6. The option(s) with the values of aa n dL that satisfy the following eq...

    Text Solution

    |

  7. Let F:R- R be a thrice differentiable function. Suppose that F(1)=0,F(...

    Text Solution

    |

  8. Let F : R to R be a thrice differentiable function . Suppose that F(...

    Text Solution

    |

  9. Let f: RvecR be a function defined by f(x)={[x],xlt=2 0,x >2 where [...

    Text Solution

    |

  10. If alpha=int0^1(e^9x+3tan^((-1)x))((12+9x^2)/(1+x^2))dxw h e r etan^(-...

    Text Solution

    |

  11. The integral overset(pi//2)underset(pi//4)int (2 cosecx)^(17)dx is equ...

    Text Solution

    |

  12. Let f:[0,2]vecR be a function which is continuous on [0,2] and is diff...

    Text Solution

    |

  13. Match the conditions/ expressions in Column I with statement in Column...

    Text Solution

    |

  14. Match List I with List II and select the correct answer using codes gi...

    Text Solution

    |

  15. The value of int0^1 4x^3{(d^2)/(dx^2)(1-x^2)^5}dxi s

    Text Solution

    |

  16. The value of the integral int(-pi//2)^(pi//2) (x^(2) + log" (pi-x)/(pi...

    Text Solution

    |

  17. The value of int(sqrt(ln2))^(sqrt(ln3)) (xsinx^2)/(sinx^2+sin(ln6-x^2)...

    Text Solution

    |

  18. Let f:[1,oo] be a differentiable function such that f(1)=2. If int1...

    Text Solution

    |

  19. The value of int(0)^(1) (x^(4)(1-x)^(4))/(1+x^(2)) dx is (are)

    Text Solution

    |

  20. For a in R ( the set of all real number) , a ne -1, lim(n to oo)((1^...

    Text Solution

    |

  21. Consider the statements : P : There exists some x IR such that f(x)...

    Text Solution

    |