Home
Class 12
MATHS
If f(x) = (e^x)/(1 + e^x) , I1 = int(f(-...

If `f(x) = (e^x)/(1 + e^x) , I_1 = int_(f(-a))^(f(a)) x g {x(1 - x)} dx and I_2 = int_(f(-a))^(f(a)) g{x(1 - x)} dx`, then `(I_2)/(I_1)` is :

A

2

B

minus 3

C

minus 1

D

1

Text Solution

Verified by Experts

The correct Answer is:
A
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

f(x) = ((e^(2x)-1)/(e^(2x)+1)) is

int (f^(')(x))/(f(x) log [f(x)]) dx =

Let I_(1) = int_a^(pi-a) xf (sin x) dx, I_(2) = int_a^(pi-a) f(sinx) dx then I_(2) is equal to

If I_(1) = int_e^(e^(2)) (dx)/(log x) and I_(2) = int_1^(2) (e^(x)dx)/(x) then

If d/(dx) f(x) = g (x) , then int_a^b f(x) g(x) dx is:

If int_(-1)^(4) f(x) dx = 4 and int_(2)^(4) f(x) dx = 7 then int_2^(-1) f(x) dx =

If int f(x) dx = f(x) , then int {f(x)}^(2) dx =

Let f(x) = (e^(x)+1)/(e^(x)-1) and int_0^(1)( (e^(x)+1)/(e^(x)-1)) x dx = lambda , then int_(-1)^(1) t f(t) dt =

If 2f(x)- 3f(1/x) = x then int_1^(e) f(x) dx =

HIMALAYA PUBLICATION-Definite Integrals and its Application-QUESTION BANK
  1. If f(y) = e^(y), g(y) = y , y > 0 and F(t) = int0^t f(t - y) g(y) dy...

    Text Solution

    |

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

    Text Solution

    |

  3. If f(x) = (e^x)/(1 + e^x) , I1 = int(f(-a))^(f(a)) x g {x(1 - x)} dx a...

    Text Solution

    |

  4. The value of I = int0^(pi//2) ((sin x + cos x)^2)/(sqrt(1 + sin 2x)) d...

    Text Solution

    |

  5. The value of int(-2)^3 |1 - x^2| dx is:

    Text Solution

    |

  6. If int0^pi x f (sin x)dx = A int0^(pi//2) f (sin x) dx, then A is :

    Text Solution

    |

  7. Let F : R to R be a differentiable function having : f(2) = 6, f'(2) =...

    Text Solution

    |

  8. int0^(pi) x f (sin x) dx is equal to :

    Text Solution

    |

  9. int(-3pi//2)^(-pi//2) [(x +pi)^3 + cos^2 (x + 3x)]dx is equal to :

    Text Solution

    |

  10. If f(x) ={(e^(cosx)sinx; |x| le 2),(2 ; othe...

    Text Solution

    |

  11. The value of integral int(e^(-1))^(e^2) |(loge x)/(x)| dx is :

    Text Solution

    |

  12. Let g(x) = int0^(x) f(t) dt, where 1/2 le f(t) < 1, t in [0,1] and 0 <...

    Text Solution

    |

  13. The value of int(-pi)^(pi) (cos^2 x)/(1 + a^x) dx, a > 0, is :

    Text Solution

    |

  14. Let f : (0, oo ) to R and F(x) = int0^x f(t) dt. If F(x^2) = x^2(1 +...

    Text Solution

    |

  15. Let f(x) = int1^x sqrt(2 - t^2) dt. Then the real roots of the equatio...

    Text Solution

    |

  16. The integral int(-1//2)^(1//2) ([x] + ln ((1 + x)/(1 - x)))dx equals :

    Text Solution

    |

  17. If I(m,n) = int0^1 t^m (1 + t)^n dt , m, n in R, then I(m, n) is :

    Text Solution

    |

  18. The value of the integral int0^1 sqrt((1 - x)/(1 + x))dx is :

    Text Solution

    |

  19. If f(x) is differentiable and int0^(t^2) x f(x) dx = 2/5 t^5, then f (...

    Text Solution

    |

  20. If int(sin x)^(1) t^2 f(t) dt = 1 - sin x, then the value of f(1/(sqrt...

    Text Solution

    |