Home
Class 12
MATHS
int0^1log(1+x)/(1+x^2)dx...

`int_0^1log(1+x)/(1+x^2)dx`

A

`(pi)/8log2`

B

`(pi)/8"log"1/2`

C

`(pi)/4log2`

D

`(pi)/4"log"1/2`

Text Solution

Verified by Experts

The correct Answer is:
A
Promotional Banner

Topper's Solved these Questions

  • DEFINITE INTEGRALS

    TARGET PUBLICATION|Exercise COMPETITIVE THINKING|148 Videos

  • CONTINUITY

    TARGET PUBLICATION|Exercise Evaluation Test|10 Videos

  • DIFFERENTIAL EQUATIONS

    TARGET PUBLICATION|Exercise EVALUATION TEST|25 Videos

Similar Questions

Explore conceptually related problems

Evaluate int_0^1 log(1+x)/(1+x^2)dx

The value of int_0^1(8log(1+x))/(1+x^2)dx is a. pilog2 b. \ pi/8log2 c. \ pi/2log2 d. log2

Evaluate the following integral: int_0^1("log"(1+x))/(1+x^2)dx

int_0^1 log((x)/(1-x))dx=0

The value of int_0^1 (8log(1+x))/(1+x^2) dx is:

int_(0)^(1)(log(1-x))/(x)dx

Show that :int_(0)^(1)(log x)/((1+x))dx=-int_(0)^(1)(log(1+x))/(x)dx

Evaluate: int_0^1log(x^2+x+1)dx

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

TARGET PUBLICATION-DEFINITE INTEGRALS-EVALUATIO TEST
  1. int0^1log(1+x)/(1+x^2)dx

    Text Solution

    |

  2. For every integer n, int(n)^(n+1)f(x)dx=n^(2), then the value of int(0...

    Text Solution

    |

  3. If f(x)+f(3-x)=0,then int(0)^(3)1/(1+2^(f(x)))dx=

    Text Solution

    |

  4. int(0)^(oo)(x logx)/((1+x^(2))^(2)) dx=

    Text Solution

    |

  5. Let I=int0^n[x]dx,n > 0, where [ ] is G.I.F.,

    Text Solution

    |

  6. If In = int0^(pi/2) (sin^2 nx)/(sin^2 x) dx, then

    Text Solution

    |

  7. The value of the integral intalpha^beta 1/(sqrt((x-alpha)(beta-x)))dx

    Text Solution

    |

  8. Let f(x)=(e^(x)+1)/(e^(x)-1) and int(0)^(1) x^(3) .(e^(x)+1)/(e^(x)-1)...

    Text Solution

    |

  9. If m and n are positive integers and f(m,n)=int(0)^(1)x^(n-1)(logx)^(m...

    Text Solution

    |

  10. The least value of the function phi(x)=int((7pi)/6)^(x)(4sint+3cost)dt...

    Text Solution

    |

  11. Prove that int(a)^(b)f(x)dx=(b-a)int(0)^(1)f((b-a)x+a)dx

    Text Solution

    |

  12. The integral int0^(1. 5)[x^2]dx ,w h e r e[dot] denotoes the greatest ...

    Text Solution

    |

  13. If f(x) is a function satisfying f(1/x)+x^(2)f(x)=0 for all non zero x...

    Text Solution

    |

  14. lim(ntooo)1/n[1+sqrt(n/(n+1))+sqrt(n/(n+2))+sqrt(n/(n+3))+………..+sqrt(n...

    Text Solution

    |

  15. lim(n->oo)sum(n=1)^n(sqrt(n))/(sqrt(r)(3sqrt(r)+4sqrt(n))^2)

    Text Solution

    |

  16. Let f(x) be a function satisfyingf'(x)=f(x) withf(0) =1 and g(x) be a ...

    Text Solution

    |

  17. int(0)^(100pi)(|sin^(3)x|+|cos^(3)x|)dx=

    Text Solution

    |

  18. I1=int0^(pi/2)(sinx-cosx)/(1+sinxcosx)dx ,I2=int0^(2pi)cos^6xdx ,I3=in...

    Text Solution

    |

  19. overset(2pi) underset(0)int(xsin^(2n)x)/(sin^(2n)x+cos^(2n)x)dx,n gt 0...

    Text Solution

    |

  20. The equation int(-pi/4)^(pi/4){a|sinx|+(bsinx)/(1+cos^2x)+c}dx=0 where...

    Text Solution

    |