Home
Class 12
MATHS
the integral int0^(1/2) (ln(1+2x))/(1+4x...

the integral `int_0^(1/2) (ln(1+2x))/(1+4x^2) dx` equals

A

`(pi)/(4) log 2`

B

`(pi)/( 8) log 2`

C

`(pi)/( 16) log 2`

D

`(pi)/( 32) log 2`

Text Solution

Verified by Experts

The correct Answer is:
C
Promotional Banner

Topper's Solved these Questions

  • DEFINITE INTEGRALS

    MCGROW HILL PUBLICATION|Exercise Questions from Previous Years. B-Architecture Entrance Examination Papers|18 Videos

  • DEFINITE INTEGRALS

    MCGROW HILL PUBLICATION|Exercise EXERCISE (LEVEL 2) Numerical Answer Type Questions|19 Videos

  • COMPLEX NUMBERS

    MCGROW HILL PUBLICATION|Exercise QUESTIONS FROM PREVIOUS YEARS. B-ARCHITECTURE ENTRANCE EXAMINATION PAPER|17 Videos

  • DETERMINANTS

    MCGROW HILL PUBLICATION|Exercise QUESTIONS FROM PREVIOUS YEARS B-ARCHITECTURE ENTRANCE EXAMINATION PAPERS|18 Videos

Similar Questions

Explore conceptually related problems

int_(0)^(1)(log(1+x))/(1+x^(2))dx

The value of definite integral int_(1/3)^(2/3)(ln x)/(ln(x-x^(2)))dx is equal to :

The value of definite integral int_(1/3)^(2/3)(ln x)/(ln(x-x^(2)))dx is equal to

The value of definite integral int_(1/3)^(2/3)(ln x)/(ln(x-x^(2)))dx is equal to:

By Simpson rule taking n=4, the value of the integral int _(0)^(1)(1)/(1+x^(2))dx is equal to

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

The integral int_(-1)^(1) (|x+2|)/(x+2)dx is equal to

MCGROW HILL PUBLICATION-DEFINITE INTEGRALS-Questions from Previous Years. AIEEE/ JEE Main Papers
  1. The integral int(7pi//4)^(7pi//3) sqrt(tan^(2) x) dx is equal to

    Text Solution

    |

  2. The integral int0^pisqrt(1+4sin^2x/2-4sinx/2dx) equal (1) pi-4 (2)...

    Text Solution

    |

  3. the integral int0^(1/2) (ln(1+2x))/(1+4x^2) dx equals

    Text Solution

    |

  4. If for n ge 1, P(n) = int(1)^( e) (log x)^(n) dx, then P(10) - 90P(8) ...

    Text Solution

    |

  5. int(0)^(pi)[cos x] dx, [ ] denotes the greatest integer function , is ...

    Text Solution

    |

  6. If for a continuous function f(x), int(-pi)^(t) (f(x)+ x) dx= pi^(2) -...

    Text Solution

    |

  7. Let function F be defined as f(x)= int1^x e^t/t dt x > 0 then the v...

    Text Solution

    |

  8. The integral int2^4(logx^2)/(logx^2+log(36-12 x+x^2)dx is equal to:...

    Text Solution

    |

  9. Let f: RR rarr RR be a function such that f(2 - x) =f(2 + x) and f(4-x...

    Text Solution

    |

  10. Let f : (-1,1) to R be continous function , if int (0)^(sinx) f(t)...

    Text Solution

    |

  11. If f(x)=underset(1)overset(x)int (log t)/(1+t) dt"then" f(x)+f((1)/(x)...

    Text Solution

    |

  12. If 2int0^1 tan^(-1)x dx= int0^1 cot^(-1)(1-x+x^2) dx then int0^1 tan^(...

    Text Solution

    |

  13. underset (n rarr infty )(lim) [((n+1)(n+2)...3n)/(n^(2n))]^(1//n) is e...

    Text Solution

    |

  14. int4^10([x^2])/([x^2-28 x+196]+[x^2])dx is (A) 3 (B) 5 (C) 7 (D) 9

    Text Solution

    |

  15. The integral int(pi/12)^(pi/4)(8cos2x)/((tanx+cotx)^3)dx equals

    Text Solution

    |

  16. If int(1)^(2) (dx)/( (x^(2) -2x + 4)^(3/2))=(k)/( k+5) then k is equal...

    Text Solution

    |

  17. int(pi//4)^(3pi//4)(dx)/(1+cos x)=

    Text Solution

    |

  18. Find a for which lim(n->oo) (1^a+2^a+3^a+...+n^a)/((n+1)^(a-1)[(na+1)+...

    Text Solution

    |

  19. If i is the greatest of the definite integrals I1=int0^1 e^-x cos ^2 ...

    Text Solution

    |

  20. The value of the integral int(-pi//2)^(pi//2) sin^(4) x (1+ log ((2+ s...

    Text Solution

    |