Home
Class 12
MATHS
Evaluate the following integral:int0^pi(...

Evaluate the following integral:`int_0^pi(xtanx)/(secx\ cos e c\ x)dx`

Text Solution

Verified by Experts

`int_0^pi(xtanx)/(secx\ cos e c\ x)dx`
`=int_0^pi x sn^2x dx ---(1)`
`I=int_0^pi(pi-x)sin^2(pi-x)dx`
`2I=int_0^pi pi sin^2 dx`
`I=pi/2 int_)^pi sin^2x dx`
`=(pi^)/4-pi/8 (sin 2 pi-0)`
`=(pi)^2/4`
Promotional Banner

Topper's Solved these Questions

  • CONTINUITY

    RD SHARMA|Exercise Solved Examples And Exercises|277 Videos
  • DERIVATIVES AS A RATE MEASURER

    RD SHARMA|Exercise Solved Examples And Exercises|149 Videos

Similar Questions

Explore conceptually related problems

Evaluate the following integral: int_0^pi(dx)/(6-cosx)

Evaluate the following integral: int_0^pi(sinx)/(sinx+cosx)dx

Evaluate the following integral: int_0^pi(xsinx)/(1+sinx)dx

Evaluate the following integral: int_0^1x e^x^2dx

Evaluate the following: int_0^pi (xtanx)/(secxcosecx)dx

Evaluate the following : int_(0)^(pi)(x tan x)/(secx+cos x)dx

Evaluate the following integral: int_0^(2pi)cos^7x\ dx

Evaluate the following integral: int_0^pilog(1-cos x)dx

Evaluate the following : int_(0)^(pi)(x tanx)/(secx "cosec x")dx

Evaluate the following integral: int_0^(pi//4)(tan^3x)/(1+cos2x)dx

RD SHARMA-DEFINITE INTEGRALS-Solved Examples And Exercises
  1. Evaluate the following integral: int0^oo(logx)/(1+x^2)dx

    Text Solution

    |

  2. Evaluate the following integral:int0^1("log"(1+x))/(1+x^2)dx

    Text Solution

    |

  3. Evaluate the following integral:int0^pi(xtanx)/(secx\ cos e c\ x)dx

    Text Solution

    |

  4. Evaluate the following integral:int0^pixsin^3x\ dx

    Text Solution

    |

  5. Evaluate the following integral:int0^pi(xsinx)/(1+sinx)dx

    Text Solution

    |

  6. Evaluate the following integral:int0^(pi//2)(tan^7x)/(tan^7x+cot^7x)dx

    Text Solution

    |

  7. Evaluate the following integral:int0^(pi//2)x\ s in xcos^2x\ dx

    Text Solution

    |

  8. Evaluate the following integral:int(-pi//2)^(pi//2)sin^3x\ dx

    Text Solution

    |

  9. Evaluate the following integral:int(-1)^1log((2-x)/(2+x))dx\

    Text Solution

    |

  10. Evaluate the following integral:int0^pilog(1-cos x)dx

    Text Solution

    |

  11. Evaluate the following integral:int(-pi)^pi(2x(1+sinx))/(1+cos^2dx)dx

    Text Solution

    |

  12. Evaluate the following integral:int0^2x\ sqrt(2-x)\ dx

    Text Solution

    |

  13. Evaluate the following integral:int0^oox/((1+x)(1+x^2))dx

    Text Solution

    |

  14. Evaluate the following integral:int0^pixsinxcos^4x\ dx

    Text Solution

    |

  15. Evaluate the following integral:int0^pixlogsinx\ dx

    Text Solution

    |

  16. Evaluate the following integral:int0^pixlogsinx\ dx

    Text Solution

    |

  17. Evaluate the following integral: int(pi/6)^(pi/3) (1/(1+cot^(3/2)x)) d...

    Text Solution

    |

  18. Evaluate the following integral:int(pi//6)^(pi//3)1/(1+cot^(3//2)x)dx

    Text Solution

    |

  19. Evaluate the following integral:int2^8(sqrt(10-x))/(sqrt(x)+sqrt(10-x)...

    Text Solution

    |

  20. Evaluate the following integral:int0^(pi//2)(xsinxcosx)/(sin^4x+cos^4x...

    Text Solution

    |