Home
Class 12
MATHS
Prove that: int0^(pi//2)logsinx\ dx=\ in...

Prove that: `int_0^(pi//2)logsinx\ dx=\ int_0^(pi//2)logcosx\ dx=-pi/2log2`

Text Solution

AI Generated Solution

Promotional Banner

Topper's Solved these Questions

  • CONTINUITY

    RD SHARMA ENGLISH|Exercise All Questions|282 Videos

  • DERIVATIVES AS A RATE MEASURER

    RD SHARMA ENGLISH|Exercise All Questions|168 Videos

Similar Questions

Explore conceptually related problems

Prove that int_(0)^(pi//2)log (sinx)dx=int_(0)^(pi//2) log (cosx)dx=-(pi)/(2) log 2 .

Evaluate: int_0^(pi//2)sinx\ dx

Prove that: int_(0)^(pi//2) log (sin x) dx =int_(0)^(pi//2) log (cos x) dx =(-pi)/(2) log 2

Evaluate: int_0^(pi//2)logtanx\ dx

Evaluate : int_0^(pi//2)sinx\ dx

Prove: int_0^(pi//2) \ log|tanx| \ dx=0

Prove that : int_(0)^(pi//2) x . cot x dx =(pi)/(2)log 2

Evaluate: int_0^(pi//2)cosx\ dx

Evaluate int_0^(pi/2) sin^2x dx

Prove that: int_0^(pi//2)log|tanx+cotx|dx=pi(log)_e2

RD SHARMA ENGLISH-DEFINITE INTEGRALS-All Questions
  1. Find the value of int(-1)^(3/2)|xsinpix|dx

    Text Solution

    |

  2. Evaluate: int0^(2pi)cos^5x\ dx

    Text Solution

    |

  3. Prove that: int0^(pi//2)logsinx\ dx=\ int0^(pi//2)logcosx\ dx=-pi/2log...

    Text Solution

    |

  4. Evaluate: int0^pilog(1+cosx)dx

    Text Solution

    |

  5. Evaluate the following integral: int0^(pi//2)1/(1+tanx)dx

    Text Solution

    |

  6. Evaluate the following integral: int0^(pi//2)(sqrt(cotx))/(sqrt(cotx\ ...

    Text Solution

    |

  7. Evaluate the following integral: int0^a1/(x+sqrt(a^2-x^2))dx

    Text Solution

    |

  8. Evaluate the following integral: int0^(pi//2)1/(1+cotx)dx

    Text Solution

    |

  9. Evaluate the following integral: int0^(pi//2)(sin^(3//2)x\ )/(sin^(3//...

    Text Solution

    |

  10. Evaluate the following integral: int0^(pi//2)1/(1+tanx)dx

    Text Solution

    |

  11. Evaluate the following integral: int0^oo(logx)/(1+x^2)dx

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

  17. Evaluate the following integral:int0^(pi//2)x\ sin xcos^2x\ dx

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |