Home
Class 12
MATHS
int (0)^(pi//2) (sin x cos xdx)/(cos^(2)...

` int _(0)^(pi//2) (sin x cos xdx)/(cos^(2) x+ 3 cos x+2)`is equal to

A

`log.((8)/(9))`

B

`log.((9)/(8))`

C

`log(8xx9)`

D

None of these

Text Solution

Verified by Experts

The correct Answer is:
B
Let `l=int_(0)^(pi//2)(sin x cosx)/(cos^(2)x+3cos x+2)dx`
Put `cos x = t rArr - sin x dx =dt`
`therefore" "l=int_(0)^(1)(t.dt)/(t^(2)+3t+2)=int_(0)^(1)[(1)/(t+2)-(1)/(t+1)]dt`
`l=[2log(t+2)-log(t+1)]_(0)^(1)`
`l=2log3-3log2-2log2`
`l=log 9-log8=log((9)/(8))`
Promotional Banner

Topper's Solved these Questions

  • DEFINITE INTEGRALS

    MHTCET PREVIOUS YEAR PAPERS AND PRACTICE PAPERS|Exercise PRACTICE EXERCISE (Exercise 2) (MISCELLANEOUS PROBLEMS)|76 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/2)x sin x cos xdx

int_(0)^(pi//2)(sin x cos x dx)/(cos^(2)x+3cosx+2)=

int_(0)^((pi)/(2))x sin x cos xdx

int_(0)^( pi/2)sin^(2)x cos xdx

int_(0)^( pi/2)sin^(3)x cos xdx=

int_(0)^( pi/2)sin x*cos^(3)xdx

int_(0)^( pi)x sin x cos^(2)xdx

int_(0)^( pi/2)sin^(3)x cos xdx=?

int_(0)^( pi/2)sin^(3)x cos xdx=?

int_(0)^( pi/2)sin^(3)x cos xdx=?

MHTCET PREVIOUS YEAR PAPERS AND PRACTICE PAPERS-DEFINITE INTEGRALS-MHT CET Corner
  1. int (0)^(pi//2) (sin x cos xdx)/(cos^(2) x+ 3 cos x+2)is equal to

    Text Solution

    |

  2. int (-pi/2)^(pi/2)log((2-sin x)/(2+sinx))dx is equal to

    Text Solution

    |

  3. int (0)^(pi //2)((root(n)(secx))/(root(n)(secx)+root(n)("cosec"x)))dx=

    Text Solution

    |

  4. The value of int 0 ^ 1 x ^ 2 ( 1 - x ^ 2 ) ^ (3//2 ) dx ...

    Text Solution

    |

  5. The value of int0^oox/((1+x)(x^2+1))dx is

    Text Solution

    |

  6. Evaluate int(0)^(pi)(x dx)/(1+cos alpha sin x),where 0lt alpha lt pi.

    Text Solution

    |

  7. int(pi//2)^(pi//2)(cosx)/(1+e^(x))dx is equal to

    Text Solution

    |

  8. int(0)^(pi//2)(1)/((1+tanx))dx=?

    Text Solution

    |

  9. If int(0)^(1) tan^(-1) x dx = p , then the value of int(0)^(1) tan^(-1...

    Text Solution

    |

  10. The value of int (0)^(pi//2) log ("cosec "x) dx is

    Text Solution

    |

  11. Which of the following is true ?

    Text Solution

    |

  12. int(0)^(5) 1/((x-1)(x-2))dx is equal to

    Text Solution

    |

  13. int(pi/4)^(pi/2) e^x(logsinx+cotx)dx

    Text Solution

    |

  14. The value of int(0)^(pi) x sin^(3) x dx is

    Text Solution

    |

  15. The value of int0 ^(pi/2) (cos3x+1)/(cosx - 1) dx is equal to

    Text Solution

    |

  16. The value of underset(0)overset(1)int tan^(-1) ((2x-1)/(1+x-x^(2)))dx ...

    Text Solution

    |

  17. If f is a continous function, then

    Text Solution

    |

  18. The value of int(-pi)^(pi) sin^(3) x cos^(2) x dx is equal to

    Text Solution

    |

  19. The value of int(-1)^(1) log ((x-1)/(x+1))dx is

    Text Solution

    |

  20. int(pi//6)^(pi//3)(1)/((1+sqrt(tanx)))dx=(pi)/(12)

    Text Solution

    |

  21. int (1)^(2)e^(x) (1/x - 1/(x^(2)))dx is qual to

    Text Solution

    |