Home
Class 12
MATHS
The integral int(2)^(4)(logx^(2))/(logx^...

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

A

1

B

6

C

2

D

4

Text Solution

Verified by Experts

The correct Answer is:
A
`overset(4)underset(2)int (logx^(2))/(log x^(2) +log(36-12x+x^(2)))dx`.Then,
`I=overset(4)underset(2)int (logx^(2))/(logx^(2)+log(36-12x+x^(2)))dx`
Clearly, it is of the form `overset(b)underset(a)int (f(x))/(f(x)+f(a+b-x))dx` where
f(x)`=logx^(2)`,a=2 and b=4.
We know that `overset(b)underset(a)int (f(x))/(f(x)+f(a+b-x))dx=(b-a)/(2)`
`:. I=(4-2)/(2)=1`.
Promotional Banner

Topper's Solved these Questions

  • DEFINITE INTEGRALS

    OBJECTIVE RD SHARMA ENGLISH|Exercise Section I - Solved Mcqs|145 Videos

  • DEFINITE INTEGRALS

    OBJECTIVE RD SHARMA ENGLISH|Exercise Section II - Assertion Reason Type|12 Videos

  • CONTINUITY AND DIFFERENTIABILITY

    OBJECTIVE RD SHARMA ENGLISH|Exercise Exercise|87 Videos

  • DERIVATIVE AS A RATE MEASURER

    OBJECTIVE RD SHARMA ENGLISH|Exercise Exercise|26 Videos

Similar Questions

Explore conceptually related problems

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

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

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

int(log(x+1)-logx)/(x(x+1))dx is equal to :

The value of int_(0)^(oo)(logx)/(a^(2)+x^(2))dx is

The value of int_(0)^(oo) (logx)/(1+x^(2))dx , is

int(x^(2)(1-logx))/((logx)^(4)-x^(4))dx equals

int((x+1)(x+logx)^2)/(2x)dx

int(logx/(1+logx)^2)dx

Evaluate int((x+1)/(x))(x+logx)^(2)dx

OBJECTIVE RD SHARMA ENGLISH-DEFINITE INTEGRALS-Chapter Test 2
  1. The integral int(2)^(4)(logx^(2))/(logx^(2)+log(36-12x+x^(2))) dx is e...

    Text Solution

    |

  2. The value of the integral int(0)^(2)x[x]dx

    Text Solution

    |

  3. The value of integral sum (k=1)^(n) int (0)^(1) f(k - 1+x) dx is

    Text Solution

    |

  4. Let f (x) be a function satisfying f(x)=f(x) with f(0) = 1 and g be th...

    Text Solution

    |

  5. If I=int(0)^(1)cos(2 cot^(-1)sqrt(((1-x)/(1+x))))dx then :

    Text Solution

    |

  6. The value of int(a)^(a+(pi//2))(sin^(4)x+cos^(4)x)dx is

    Text Solution

    |

  7. The vaue of int(-1)^(2) (|x|)/(x)dx is

    Text Solution

    |

  8. The value of int0^1 (x^(3))/(1+x^(8))dx is

    Text Solution

    |

  9. The value of int(0)^(3) xsqrt(1+x)dx, is

    Text Solution

    |

  10. Evaluate int(0)^(1)log(sin((pix)/(2)))dx

    Text Solution

    |

  11. Evaluate int(0)^(pi) xlog sinx dx

    Text Solution

    |

  12. If I(1)=int(0)^(oo) (dx)/(1+x^(4))dx and I(2)=underset(0)overset(oo)i...

    Text Solution

    |

  13. If f(x)={{:(x,xlt1),(x-1,xge1):}, then underset(0)overset(2)intx^(2)f(...

    Text Solution

    |

  14. The value of the integral overset(1)underset(0)int (1)/((1+x^(2))^(3//...

    Text Solution

    |

  15. Prove that: int0^(2a)f(x)dx=int0^(2a)f(2a-x)dxdot

    Text Solution

    |

  16. If int(0)^(36) (1)/(2x+9)dx =log k, is equal to

    Text Solution

    |

  17. The value of the integral int(0)^(pi//2) sin^(6) x dx, is

    Text Solution

    |

  18. If int(0)^(oo) e^(-x^(2))dx=sqrt((pi)/(2))"then"int(0)^(oo) e^(-ax^(2)...

    Text Solution

    |

  19. The value of the integral int 0^oo 1/(1+x^4)dx is

    Text Solution

    |

  20. The value of alpha in [0,2pi] which does not satify the equation int(p...

    Text Solution

    |

  21. lim(x to 0)(int(0)^(x^(2))sinsqrt(t) dt)/(x^(3)) is equl to

    Text Solution

    |