Home
Class 12
MATHS
Let F(x) = f(x) + f(1/x), where , f(x) =...

Let `F(x) = f(x) + f(1/x)`, where , `f(x) = int_1^x (log t)/(1 + t) dt`. Then `F(e )` equals :

A

0

B

1

C

z

D

`1/2`

Text Solution

Verified by Experts

The correct Answer is:
D
Promotional Banner

Topper's Solved these Questions

  • DEFINITE INTEGRALS

    MODERN PUBLICATION|Exercise LATEST QUESTIONS FROM AIEEE/JEE EXAMINATION|13 Videos

  • DEFINITE INTEGRALS

    MODERN PUBLICATION|Exercise RECENT COMPETITIVE QUESTIONS|21 Videos

  • DEFINITE INTEGRALS

    MODERN PUBLICATION|Exercise RECENT COMPETITIVE QUESTIONS|21 Videos

  • COMPLEX NUMBERS

    MODERN PUBLICATION|Exercise Questions from karnataka CET & COMED|15 Videos

  • DETERMINANTS

    MODERN PUBLICATION|Exercise Recent competitive Questions|10 Videos

Similar Questions

Explore conceptually related problems

If F(x) = int_3^x (2 + d/(dt) cos t)dt , then F' (pi/6) equals :

Let, f(x) = int_0^(x) (cos t)/t dt . Then x = (2n+1) pi/2 , f(x) has

Let f(x) = x - 1/x , then f' (-1) is

If f(x) = 1 - 1/x , then f(f(1/x)) =

If f(x) = int_(0)^(x) t sin t dt, then f'(x) is

If f(x) = (x-1)/(x+1) , then f[1/f(x)] =

If f(x) = (x-3)/(x+1) , then f[f{f(x)}] =

If f(x) = int_(2x)^(sinx) cos (t^(3)) dt then f '(x)

For x in 0,(5pi/(2)), define f(x) = int_0^x sqrt(t) sin t dt . Then f has :

Let f(x) = 1-x^5 , then f(x).f(1/x) =

MODERN PUBLICATION-DEFINITE INTEGRALS-MULTIPLE CHOICE QUESTIONS (LEVEL - II)
  1. Let T > 0 be a fixed real number. Suppose f is a continuous function s...

    Text Solution

    |

  2. Let d/(dx) F(x) = ((e^(sin x))/(x)) , x > 0. If int1^4 3/x e^(sin x^3)...

    Text Solution

    |

  3. If f(y) = e^(y), g(y) = y , y > 0 and F(t) = int0^t f(t - y) g(y) dy...

    Text Solution

    |

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

    Text Solution

    |

  5. If f(x) = int(x^2)^(x^2 + 1) e^(-t^2) dt, find the interval in which f...

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

  8. If I(1) = int0^(1) 2^(x^(2)) dx, I(2) = int0^(1) 2^(x^(3)) dx, I(3) = ...

    Text Solution

    |

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

    Text Solution

    |

  10. lim(n to oo) [1/(n^2) "sec"^2 1/(n^2) + 2/(n^2) "sec"^(2) 4/(n^2) + ……...

    Text Solution

    |

  11. Let F(x) = f(x) + f(1/x), where , f(x) = int1^x (log t)/(1 + t) dt. Th...

    Text Solution

    |

  12. The solution for x of the equation : int(sqrt2)^(x) (dt)/(tsqrt(t^2 - ...

    Text Solution

    |

  13. Let I = int0^1 (sin x)/(sqrtx) dx and J = int0^1 (cos x)/(sqrtx) dx. T...

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

  16. int(-2)^(0) {x^3 + 3x^2 + 3x + 3 + (x + 1) cos (x + 1)} dx is equal to...

    Text Solution

    |

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

    Text Solution

    |

  18. The value of intI^a [x] f' (x) dx, a > 1, where [x] denotes the greate...

    Text Solution

    |

  19. int0^(pi) [cot x] dx, when [cdot] denotes the greatest integer functio...

    Text Solution

    |

  20. Let 'f' be a non-negative function defined on the interval [0,1]. If...

    Text Solution

    |