Home
Class 12
MATHS
The value of int (0)^(pi) (dx)/(5+4 cos...

The value of ` int _(0)^(pi) (dx)/(5+4 cos x ) ` is

A

`2pi`

B

`(3pi)/2`

C

`(5pi)/4`

D

`pi/3`

Text Solution

Verified by Experts

The correct Answer is:
D
Put tan `(x)/(2)=t`
`therefore " " dx=(2dt)/(1+t^(2))` and `cos x = (1-t^(2))/(1+t^(2))`
`therefore " " int_(0)^(pi)(dx)/(5+4 cos x)=int_(0)^(oo)(2dt)/(9+t^(2))`
`= [(2)/(3)tan^(-1)((t)/(3))]_(0)^(oo)=(2)/(3)(tan^(-1)oo-0)=(pi)/(3)`.
Promotional Banner

Topper's Solved these Questions

  • DEFINITE INTEGRALS

    MHTCET PREVIOUS YEAR PAPERS AND PRACTICE PAPERS|Exercise MHT CET Corner|22 Videos

  • DEFINITE INTEGRALS

    MHTCET PREVIOUS YEAR PAPERS AND PRACTICE PAPERS|Exercise MHT CET Corner|22 Videos

  • CONTINUITY

    MHTCET PREVIOUS YEAR PAPERS AND PRACTICE PAPERS|Exercise MHT CET Corner|16 Videos

  • DIFFERENTIAL EQUATION

    MHTCET PREVIOUS YEAR PAPERS AND PRACTICE PAPERS|Exercise MHT CET Corner|27 Videos

Similar Questions

Explore conceptually related problems

int_(0)^(pi) (1)/(5+2 cos x)dx

int_(0)^(pi//2) (1)/(4+3 cos x)dx

The value of int_(0)^(pi) |cos x|dx , is

int_(0)^(pi//2)(1)/(5+4cos x)dx=

The value of int_(0)^(2pi)cos^(5)x dx , is

The value of int_(0)^(pi)|cos x|^(3)dx is :

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

int_(0)^(pi//4)(dx)/((1+cos2x))

int_(0)^(pi)sin 5 x cos 4x dx=

MHTCET PREVIOUS YEAR PAPERS AND PRACTICE PAPERS-DEFINITE INTEGRALS-PRACTICE EXERCISE (Exercise 2) (MISCELLANEOUS PROBLEMS)
  1. If 2f(x) - 3 f(1//x) = x," then " int(1)^(2) f(x) dx is equal to

    Text Solution

    |

  2. int (0)^(2pi) sin^(6) x cos^(5) x dx is equal to

    Text Solution

    |

  3. int (-3pi//2)^(-pi//2) [ ( x + pi)^(3) + cos^(2) x ] dx is equalt to

    Text Solution

    |

  4. int (0)^(3) (3x+1)/(x^(2)+9) dx =

    Text Solution

    |

  5. underset(n to oo)lim underset(r=1)overset(n)sum(1)/(n)e^(r//n) is

    Text Solution

    |

  6. int (-1//2)^(1//2) cos x log ((1+x)/(1-x)) dx = k log 2 , then k equ...

    Text Solution

    |

  7. The value of the integral int (0)^(pi//2) sin ^(5) x dx is

    Text Solution

    |

  8. If int (0)^(x^(2)) f(t) dt = x cos pix , then the value of f(4) is

    Text Solution

    |

  9. If f(x) is differentiable and int0^(t^2)xf(x)dx=2/5t^5, then f(4/(25))...

    Text Solution

    |

  10. The value of int (0)^(pi//2) sin ^(8) x dx is

    Text Solution

    |

  11. The value of overset(pi)underset(-pi)int(1-x^(2)) sin x cos^(2) x" dx"...

    Text Solution

    |

  12. int (0)^(1) (xdx)/([x + sqrt(1-x^(2))]sqrt(1-x^(2))) is equal to

    Text Solution

    |

  13. The value of int(0)^(pi)(Sigma(r=0)^(3)a(r)cos^(3-r)x sin^(r)x)dx depe...

    Text Solution

    |

  14. The value of int (-1)^(1) x|x| dx is

    Text Solution

    |

  15. The value of integral int (1//pi)^(2//pi)(sin(1/x))/(x^(2))dx=

    Text Solution

    |

  16. The value of int (1)^(e^(2)) (dx)/(x(1+ log x)^(2) ) is

    Text Solution

    |

  17. int(pi//3)^(pi//2) (sqrt(1+cosx))/((1-cosx)^(5//2)) dx

    Text Solution

    |

  18. The value of the integral overset(1)underset(0)int x(1-x)^(n)dx, is

    Text Solution

    |

  19. The value of int (0)^(pi) (dx)/(5+4 cos x ) is

    Text Solution

    |

  20. The integral int (0)^(1) (dx)/(1-x+x^(2)) has the value

    Text Solution

    |