Home
Class 12
MATHS
If int0^1 (e^t)/(1 + t) dt = a, then int...

If `int_0^1 (e^t)/(1 + t) dt = a,` then `int_0^1 (e^t)/((1 + t)^(2))dt` is equal to:

A

a-1+e/2

B

a+1-e/2

C

a-1-e/2

D

a+1+ e/2

Text Solution

Verified by Experts

The correct Answer is:
B
Promotional Banner

Topper's Solved these Questions

  • COORDINATE SYSTEMS, LOCUS AND STRAIGHT LINES

    HIMALAYA PUBLICATION|Exercise QUESTION BANK|297 Videos

  • DIFFERENTIAL EQUATIONS

    HIMALAYA PUBLICATION|Exercise QUESTION BANK|206 Videos

Similar Questions

Explore conceptually related problems

int_(0)^(1)(dx)/(e^(x)+e^(-x)) is equal to

Let A = int_0^(1) e^(t)/(t+1) dt , then int_0^(1) (t.e^(t^(2)))/(t^(2)+1) dt =

int_0^(1) x^(2).e^(x) dx =

int (1+t^(2))/(1+t^(4))dt =

int_0^1(dx)/(e^x+e^(-x)) is equal to

The value of int_0^1 (1 + e^(-x^2)) dx is :

HIMALAYA PUBLICATION-Definite Integrals and its Application-QUESTION BANK
  1. If x=int0^(y) (dt)/(sqrt(1+9t^(2))) and (d^(2)y)/(dx^(2)) = ay, then a...

    Text Solution

    |

  2. int(-1)^(1) (x^3 + |x| + 1)/(x^2 + 2|x| + 1) dx is equal to :

    Text Solution

    |

  3. If int0^1 (e^t)/(1 + t) dt = a, then int0^1 (e^t)/((1 + t)^(2))dt is e...

    Text Solution

    |

  4. int(-2)^2 |x cos pi x|dx is equal to :

    Text Solution

    |

  5. int(-pi//4)^(pi//4)(dx)/(1+cos 2x) is equal to

    Text Solution

    |

  6. int(0)^(pi//4) sqrt(1 -sin 2x dx) is equal to :

    Text Solution

    |

  7. Choose the correct answer int(1)^(sqrt3)(dx)/(1+x^(2)) equals

    Text Solution

    |

  8. Choose the correct answer int(0)^(2/3)(dx)/(4+9x^(2)) equals

    Text Solution

    |

  9. If f(x) = int(0)^(x) t sin t dt, then f'(x) is

    Text Solution

    |

  10. Choose the correct answer The value of the integral int(1/3)^(1)((x-...

    Text Solution

    |

  11. Choose the correct answer The value of int((-pi)/2)^(pi/2)(x^(3)+xco...

    Text Solution

    |

  12. The value of int0^(pi/2) log ((4+3sinx)/(4+3cosx)) dx is

    Text Solution

    |

  13. If f(a + b - x) = fx, then inta^b x f(x) dx is equal to :

    Text Solution

    |

  14. The value of int0^(1) tan^(-1) ((2x-1)/(1+x-x^(2))) dx is

    Text Solution

    |

  15. lim(n rarr oo) sum(r=1)^(n) r/n^(2) sec^(2) (r^(2)/n^(2)) =

    Text Solution

    |

  16. lim(n rarr oo) 1/2 [(n+1)(n+2)…….2n]^(1/n) =

    Text Solution

    |

  17. lim(n rarr oo)[(1+1/n)(1+2/n)…..2]^(1/n) =

    Text Solution

    |

  18. lim(n rarr oo) 1/n^(100) (1^(99)+2^(99)+3^(99)+………+n^(99)) =

    Text Solution

    |

  19. lim(n to oo) sum(r = 1)^(n) 1/n e^(r/n) is :

    Text Solution

    |

  20. lim(n rarr oo) sum(r=1)^(n) 1/n sec^(2) ((rpi)/(4n)) =

    Text Solution

    |