Home
Class 12
MATHS
The integral int2^4(logx^2)/(logx^2+lo...

The integral `int_2^4(logx^2)/(logx^2+log(36-12 x+x^2)dx` is equal to:

A

2

B

4

C

1

D

6

Text Solution

Verified by Experts

The correct Answer is:
C
Let ` I = int_(2)^(4)(log x^(2))/(log x^(2)+log(36-12x+x^(2)))dx`
` = int_(2)^(24) (2log x^(2))/(2 log x +log(6-x)^(2))dx`
` = int_(2)^(4)(2logx dx)/(2[logx+log(6-x)])dx" "`…(i)
` rArr I = int_(2)^(4)(log(6-x))/(log(6-x)+log_(x))dx " "` ...(ii)
` [ :' int_(a)^(b)f(x)dx= int_(a)^(b)f(a+b-x)dx]`
On adding Eqs. (i) and (ii), we get
` rArr 2I = int_(2)^(4)dx= [x] _(2)^(4) rArr 2I =2 rArr I = 1`
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

The integral int_(2)(4)(logx^(2))/(logx^(2)+log(36-12x+x^(2))) dx is equal to

The integral int_(2)^(4)(log x^(2))/(log x^(2)+log(36-12x+x^(2)))dx is equal to: (1)2(2)4(3)1(4)6

The value of the integral int(e^(5logx)-e^(4logx))/(e^(3logx)-e^(2logx))dx is equal to (A) x^2+c (B) x^3/3+c (C) x^2/2+c (D) none of these

int _(2) ^(4) (log x ^(2))/( log x ^(2) + log (36-12 x + x ^(2)) dx is

The integral int_(2)^(4)(e^(x^(2)))/(e^(x^(2))+e^((36-12x+x^(2))))dx is equal to

int{(logx-1)/(1+(logx)^(2))}^(2) dx is equal to

int_(1)^(2)(logx)/(x)dx

int_(1)^(2)(logx)/(x)dx

int_a^b logx/x^2dx

MHTCET PREVIOUS YEAR PAPERS AND PRACTICE PAPERS-DEFINITE INTEGRALS-MHT CET Corner
  1. The integral int2^4(logx^2)/(logx^2+log(36-12 x+x^2)dx 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

    |