Home
Class 12
MATHS
Prove that : int(0)^(pi) x cos^(2) x dx...

Prove that : ` int_(0)^(pi) x cos^(2) x dx =(pi^(2))/(4)`

Text Solution

AI Generated Solution

Promotional Banner

Topper's Solved these Questions

  • INTEGRATION

    NAGEEN PRAKASHAN ENGLISH|Exercise Exercise 7q|8 Videos

  • INTEGRATION

    NAGEEN PRAKASHAN ENGLISH|Exercise Exercise 7r|25 Videos

  • INTEGRATION

    NAGEEN PRAKASHAN ENGLISH|Exercise Exercise 7o|30 Videos

  • DIFFERENTIAL EQUATIONS

    NAGEEN PRAKASHAN ENGLISH|Exercise Miscellaneous Exercise|18 Videos

  • INVERES TRIGONOMETRIC FUNCTIONS

    NAGEEN PRAKASHAN ENGLISH|Exercise Miscellaneous Exercise (prove That )|9 Videos

Similar Questions

Explore conceptually related problems

int_(0)^(pi/2) cos^(2) x dx

int_(0)^(pi//4) cos^(2) x dx

Prove that :int_(0)^(pi) (x)/(1 +sin^(2) x) dx =(pi^(2))/(2sqrt(2))

int_(0)^(pi) xsin x cos^(4)x dx=

Prove that : int_(0)^(pi) (x sin x)/(1+cos^(2)x) dx =(pi^(2))/(4)

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

int_(0)^(pi) x sin x cos^(2)x\ dx

int_(0)^(pi/2) cos 2x dx

Prove that : int_(0)^(pi) sin^(2) x . cos x dx =0

int_(0)^(pi//2) x^(2) cos x dx

NAGEEN PRAKASHAN ENGLISH-INTEGRATION-Exercise 7p
  1. Prove that: int(0)^(pi//2) (1)/(1+tan^(3)x)=(pi)/(4)

    Text Solution

    |

  2. Prove that : int(0)^(pi//2) (sin x-cos x)/(1+sin x cos x)dx=0 " (ii)...

    Text Solution

    |

  3. Prove that : int(0)^(pi) x cos^(2) x dx =(pi^(2))/(4)

    Text Solution

    |

  4. Prove that : int(0)^(a) (sqrt(x))/(sqrt(x)+sqrt(a-x))dx=(a)/(2)

    Text Solution

    |

  5. Prove that : int(0)^(pi) sin^(2) x . cos x dx =0

    Text Solution

    |

  6. Prove that : int(0)^(pi//2) (sin x -cos x) log (sin^(3) x + cos^(3)x) ...

    Text Solution

    |

  7. Prove that : int(0)^(pi) sin^(2m) x. cos^(2m+1) x dx=0

    Text Solution

    |

  8. Prove that : int(2)^(7) (sqrt(x))/(sqrt(9-x)+sqrt(x))dx=(5)/(2)

    Text Solution

    |

  9. Prove that : int(pi//4)^(3pi//4) (1)/(1+cos x) dx = 2

    Text Solution

    |

  10. Evaluate : int((pi)/(4))^((3pi)/(4))(x)/(1+sinx)dx

    Text Solution

    |

  11. Prove that : int(0)^(pi) (x sin x)/(1+cos^(2)x) dx =(pi^(2))/(4)

    Text Solution

    |

  12. Prove that : int(0)^(pi//2)(x)/(sin x +cos x)dx= (pi)/(4sqrt(2)) log |...

    Text Solution

    |

  13. Prove that : int(0)^(a) (dx)/(x+sqrt(a^(2)-x^(2)))=(pi)/(4)

    Text Solution

    |

  14. Prove that int0^(pi/2) \ sin^2 x / (1+sin x cos x) \ dx = pi/(3 sqrt(3...

    Text Solution

    |

  15. Evaluate : int(0)^(1) (1-x)^(3//2) dx

    Text Solution

    |

  16. Evaluate : int(0)^(1)log ((1)/(x) -1) dx

    Text Solution

    |

  17. Evaluate : int0^1x(1-x)^5dx

    Text Solution

    |

  18. Evaluate : int(0)^(4) x(4-x)^(3//2)dx

    Text Solution

    |

  19. Prove that :(i) int(-pi)^(pi) x^(10) sin^(7) x dx =0 (ii) int(-pi)^(...

    Text Solution

    |

  20. Evaluate : int0^pi(xtan\ x)/(sec\ x+tan\ x)\ dx

    Text Solution

    |