Home
Class 12
MATHS
Let f be a non-constant continuous funct...

Let f be a non-constant continuous function for all `xge0`. Let f satisfy the relation `f(x)f(a-x)=1` for some `ainR^+`. Then `I=int_0^a(dx)/(1+f(x))` isd equal to

A

a

B

`(a)/(4)`

C

`(a)/(2)`

D

`f(a)`

Text Solution

Verified by Experts

The correct Answer is:
C
Promotional Banner

Topper's Solved these Questions

  • QUESTION PAPER 2017

    CHHAYA PUBLICATION|Exercise UNIT-4|4 Videos

  • QUESTION PAPER 2017

    CHHAYA PUBLICATION|Exercise UNIT-2|6 Videos

  • QUESTION PAPER -2018

    CHHAYA PUBLICATION|Exercise WBJEE|45 Videos

  • QUESTIONS PAPER -2019

    CHHAYA PUBLICATION|Exercise WBJEE 2019|45 Videos

Similar Questions

Explore conceptually related problems

let f(x) be a continuous function such that f(a-x)+f(x)=0 for all x in[0,a] then int_0^a dx/(1+e^f(x) is equal to

If a continuous function f on [0, a] satisfies f(x)f(a-x)=1, a >0, then find the value of int_0^a(dx)/(1+f(x))

if f(x) is a function such that f(x+k)=f(x) for K in I^+ and I=int_0^k f(x)dx then I=int_0^(k^(2-k))f(x)dx is equal to

A Function f(x) satisfies the relation f(x)=e^x+int_0^1e^xf(t)dtdot Then (a) f(0) 0

Let f:[1,3] toR be a continuous function that is differentiable in (1,3)" and " f'(x)=|(f(x))|^2+4" for all "x in(1,3) . Then,

Let f(x) be a continuous function defined for 1 le x le 3. If f(x) takes rational values for all x and f(2) = 10, then f(1,5) is equal to

Let f(x) be a continuous periodic function with period T. Let I= int_(a)^(a+T) f(x)dx . Then

A real valued function f (x) satisfied the functional relation f (x-y)=f (x)f(y) -f(a-x) f(a+y) where a is a given constant and f(0) =1. Then f (2a-x) is equal to-

Let f and g be continuous fuctions on [0, a] such that f(x)=f(a-x)" and "g(x)+g(a-x)=4 " then " int_(0)^(a)f(x)g(x)dx is equal to

CHHAYA PUBLICATION-QUESTION PAPER 2017-UNIT-3
  1. Let I1=int0^n[x]dx" and I2=int0^n{x}dx, where [x] and {x} are integral...

    Text Solution

    |

  2. Evalute : lim(ntooo)[(n)/(n^2+1^2)+(n)/(n^2+2^2)+........+(1)/(2n)].

    Text Solution

    |

  3. The value of the integral int0^1e^(x^2)dx

    Text Solution

    |

  4. int0^(100)e^(x-[x])dx=

    Text Solution

    |

  5. Solution of (x+y)^2(dy)/(dx)=a^2 ('a' being a constant ) is

    Text Solution

    |

  6. The integrating factor of the first order differential equation x^2(x^...

    Text Solution

    |

  7. If f(x)=int(-1)^x |t|dt, then for any xge0,f(x) is equal to

    Text Solution

    |

  8. Let for all xgt0,f(x)=lim(nto oo)n(x^((1)/(n))-1), then

    Text Solution

    |

  9. Let I=int0^(100pi)sqrt(1-cos2x)dx, then

    Text Solution

    |

  10. The area (sq. units) of the figure bounded by the parabolas x= -2y^2" ...

    Text Solution

    |

  11. Tangents are drawn to the ellipse (x^2)/(9)+(y^2)/(5)=1 at the ends of...

    Text Solution

    |

  12. The value of K in order that f(x)=sinx-cosx-Kx+5 decreases for all pos...

    Text Solution

    |

  13. For real x, the greatest value of (x^2+2x+4)/(2x^2+4x+9) is

    Text Solution

    |

  14. Find solution of ydx+xdy=xy(dy-dx)

    Text Solution

    |

  15. If f(x)=x^n,n being a non-negative integer, then the values of n for w...

    Text Solution

    |

  16. Let f be a non-constant continuous function for all xge0. Let f satisf...

    Text Solution

    |

  17. If the line ax+by+c=0,abne0, is a tangent to the curve xy=1-2x, then

    Text Solution

    |

  18. Two particles move in the same straight line starting at the same mome...

    Text Solution

    |

  19. If the tangents to y^2=4ax at the point (at^2,2at) where |t|>1 is a no...

    Text Solution

    |

  20. int(x^2-1)/(x^4+3x^2+1)dx(x>0) is

    Text Solution

    |