Home
Class 12
MATHS
The value of the definite integral 1/pi...

The value of the definite integral `1/pi int_(pi/2)^((5pi)/2) e^(tan^(-1)(sinx))/(e^(tan^(-1)(sinx))+e^(tan^(-1)(cosx))) dx` is

A

1

B

`pi`

C

`e`

D

`(pi)/2`

Text Solution

Verified by Experts

The correct Answer is:
B
Promotional Banner

Topper's Solved these Questions

  • DEFINITE INTEGRALS

    TARGET PUBLICATION|Exercise EVALUATIO TEST|30 Videos

  • DEFINITE INTEGRALS

    TARGET PUBLICATION|Exercise CRITICAL THINKING|115 Videos

  • CONTINUITY

    TARGET PUBLICATION|Exercise Evaluation Test|10 Videos

  • DIFFERENTIAL EQUATIONS

    TARGET PUBLICATION|Exercise EVALUATION TEST|25 Videos

Similar Questions

Explore conceptually related problems

The value of the definite integral (1)/(pi)int_((pi)/(2))^((5 pi)/(2))(e^(tan^(-1)(sin x)))/(e^(tan^(-1)(sin x)+e^(tan^(-1)(cos x)))dx is )

Evaluate the definite integrals int_(0)^((pi)/(2))sin2x tan^(-1)(sin x)dx

The value of the definite integral int_(pi//24)^(5pi//24)(dx)/(1+root(3)(tan2x)) is :

The value of the definite integral int_(2pi)^(5pi//2)(sin^(-1)(cosx)+cos^(-1)(sinx))dx is equal to

Evaluate the definite integrals int_((pi)/(2))^(pi)e^(x)((1-sin x)/(1+cos x))dx

The value of the definite integral int_(t+2pi)^(t+5pi//2) {sin^(-1)(cosx)+cos^(-1)(cosx)} dx is equal to

The value of the definite integral int_(0)^((pi)/(3))ln(1+sqrt(3)tan x)dx equals -

The value of the definite integral int_(0)^(pi//3) ln (1+ sqrt3tan x )dx equals

TARGET PUBLICATION-DEFINITE INTEGRALS-COMPETITIVE THINKING
  1. The value of overset(sqrt("In"3))underset(sqrt("In"2))int(xsinx^(2))/(...

    Text Solution

    |

  2. The value of the integral I = int(1//2014)^(2014)(tan^(-1) x)/x dx is

    Text Solution

    |

  3. The value of the definite integral 1/pi int(pi/2)^((5pi)/2) e^(tan^(-...

    Text Solution

    |

  4. If f(x)=f(pi+e-x) and inte^pif(x)dx=2/(e+pi), then inte^pi xf(x)dx is ...

    Text Solution

    |

  5. The value of int(pi//4)^(3pi//4)(phi)/(1+sinphi)d phi is

    Text Solution

    |

  6. Let I(1) =int(a)^(pi-a)xf(sinx)dx,I(2)=int(a)^(pi-a)f(sinx)dx, then I(...

    Text Solution

    |

  7. If f(x)=(e^(2))/(1+e^(x)),I(1)=overset(f(a))underset(f(-a))int xg{x(1-...

    Text Solution

    |

  8. Q. int0^pi(e^(cos^2x)( cos^3(2n+1) x dx, n in I

    Text Solution

    |

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

    Text Solution

    |

  10. If I(1)=int(0)^(pi//2)f(sin2x)sin x dx and I(2)=int(0)^(pi//4)f(cos2x)...

    Text Solution

    |

  11. Evaluate: int0^(100pi)sqrt((1-cos2x))dxdot

    Text Solution

    |

  12. int(-1)^(1) sin^(3) x cos^(2) x dx is equal to

    Text Solution

    |

  13. The value of int((pi)/4)/((-pi)/4)sin^(103)x .cos^(101)xdx is

    Text Solution

    |

  14. The value of int- 2^2(xcosx+sinx+1)dx is

    Text Solution

    |

  15. int(4)^(4)log((9-x)/(9+x))dx equals

    Text Solution

    |

  16. Evaluate the following : int(-pi//2)^(pi//2)log((2-sinx)/(2+sinx))d...

    Text Solution

    |

  17. To find the numberical value of overset(2)underset(-2)int (px^(3)+qx+8...

    Text Solution

    |

  18. If f(x)={(e^(cosx)sinx, |x|le2),(2, otherwise):} then int-2^3f(x)dx= (...

    Text Solution

    |

  19. int(-2)^0{x^3+3x^2+3x+3+(x+1)cos(x+1)dxi se q u a lto -4 (b) 0 (c...

    Text Solution

    |

  20. If f(x) is defined on [-2, 2] by f(x) = 4x^2 – 3x + 1 and g(x) = (f(-x...

    Text Solution

    |