Home
Class 12
MATHS
Show that, int(0)^(1)(1)/(x)log(1+x)dx=1...

Show that, `int_(0)^(1)(1)/(x)log(1+x)dx=1-(1)/(2^(2))+(1)/(3^(2))-(1)/(4^(2))+...oo`.

Promotional Banner

Topper's Solved these Questions

  • DEFINITE INTEGRAL

    CHHAYA PUBLICATION|Exercise EXERCISE 9B ( MULTIPLE CHOICE TYPE QUESTIONS )|6 Videos

  • DEFINITE INTEGRAL

    CHHAYA PUBLICATION|Exercise EXERCISE 9B (VERY SHORT ANSWER TYPE QUESTIONS)|20 Videos

  • DEFINITE INTEGRAL

    CHHAYA PUBLICATION|Exercise SHORT ANSWER TYPE QUESTIONS|61 Videos

  • COORDINATE GEOMETRY

    CHHAYA PUBLICATION|Exercise JEE Advanced Archive (2016)|3 Videos

  • DEFINITE INTEGRAL AS AN AREA

    CHHAYA PUBLICATION|Exercise Assertion-Reason Type|2 Videos

Similar Questions

Explore conceptually related problems

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

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

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

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

Show that : lim_(xto0)[(1)/(x)-(log(1+x))/(x^(2))]=(1)/(2)

int_(-oo)^(oo)(1)/(1+x^2) dx

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

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

int_(8)^(15)(dx)/((x-3)sqrt(x+1))=(1)/(2)log.(5)/(3)

int_(0)^(1)tan^(-1)(1-x+x^(2))dx

CHHAYA PUBLICATION-DEFINITE INTEGRAL -LONG ANSWER TYPE QUESTIONS
  1. int(0)^((3pi)/(4))(sinxdx)/(1+cos^(2)x)=(pi)/(4)+tan^(-1)((1)/(sqrt(2)...

    Text Solution

    |

  2. int(0)^((pi)/(2))sin 2x tan^(-1)(sinx)dx

    Text Solution

    |

  3. int(0)^((pi)/(4))xcosxcos3xdx=(pi+2)/(16)

    Text Solution

    |

  4. If f(x) is periodic function of period t show that int(a)^(a+t)f(x)dx ...

    Text Solution

    |

  5. If y=int(0)^(x)(t-1)(t-2)^(2)dt, find x for which (dy)/(dx)=0.

    Text Solution

    |

  6. If int(0)^(y)e^(t)dt+int(0)^(x)cost^(2)dt=0 show that, e^(y)(dy)/(dx)+...

    Text Solution

    |

  7. lim(n to oo)(1^(9)+2^(9)+3^(9)+...+n^(9))/(n^(10))

    Text Solution

    |

  8. lim(nrarroo) [(1)/(n+1)+(1)/(n+2)+(1)/(n+3)+...+(1)/(n+n)]

    Text Solution

    |

  9. lim(nrarroo) [(1)/(n)+(n^(2))/((n+1)^(3))+(n^(2))/((n+2)^(3))+...+(1)/...

    Text Solution

    |

  10. lim(nrarroo)[(n)/(n^(2)+1^(2))+(n)/(n^(2)+2^(2))+(n)/(n^(2)+3^(2))+......

    Text Solution

    |

  11. lim(nrarroo) [(1^(2))/(n^(3)+1^(3))+(2^(2))/(n^(3)+2^(3))+(3^(2))/(n^(...

    Text Solution

    |

  12. lim(nrarroo)[(n+1)/(n^(2)+1^(2))+(n+2)/(n^(2)+2^(2))+(n+3)/(n^(2)+3^(2...

    Text Solution

    |

  13. lim(nto oo)[(sqrt(n+1)+sqrt(n+2)+...+sqrt(2)n)/(sqrt(n^(3)))]

    Text Solution

    |

  14. lim(n to oo)[(1)/(sqrt(n^(2)-1^(2)))+(1)/(sqrt(n^(2)-2^(2)))+(1)/(sqrt...

    Text Solution

    |

  15. lim(nrarroo) [(1)/(n)+(sqrt(n^(2)-1^(2)))/(n^(2))+(sqrt(n^(2)-2^(2)))/...

    Text Solution

    |

  16. lim(nrarroo) [(1)/(sqrtn)+(1)/(sqrt(2n))+(1)/(sqrt(3n))+...+(1)/(n)]

    Text Solution

    |

  17. Show that, int(0)^(1)(1)/(x)log(1+x)dx=1-(1)/(2^(2))+(1)/(3^(2))-(1)/(...

    Text Solution

    |

  18. If I(m)=int(1)^(e)(logx)^(m)dx, show that, I(m)+mI(m-1)lt3.

    Text Solution

    |

  19. If u(n)=int(0)^((pi)/(4))tan^(n)xdx, show that, u(n)+u(n-2)=(1)/(n-1)(...

    Text Solution

    |

  20. If u(n)=int(0)^((pi)/(2))(sin(2n-1)x)/(sinx)dxandv(n)=int(0)^((pi)/(2)...

    Text Solution

    |