Home
Class 12
MATHS
Let f : R rarr R be a continuous functio...

Let `f : R rarr R` be a continuous function function which satisfies `f(x) = int_(0)^(x) f(t) dt`. Then the value of `f(ln5)` is

Text Solution

Verified by Experts

The correct Answer is:
0
Promotional Banner

Topper's Solved these Questions

  • DEFINITE INTEGRATION & ITS APPLICATION

    RESONANCE|Exercise Exercise 3 Part - II|25 Videos

  • DEFINITE INTEGRATION & ITS APPLICATION

    RESONANCE|Exercise High Level Problem|37 Videos

  • DEFINITE INTEGRATION & ITS APPLICATION

    RESONANCE|Exercise Exercise 2 Part - IV|9 Videos

  • COMBINATORICS

    RESONANCE|Exercise Exercise-2 (Part-II: Previously Asked Question of RMO)|8 Videos

  • DPP

    RESONANCE|Exercise QUESTION|665 Videos

Similar Questions

Explore conceptually related problems

Let f:R rarr R be a continous function which satisfies f(x)= int _(0)^(x) f (t) dt . Then , the value of f(ln5) is ______.

Let f:R rarr R be a continuous function which satisfies f(x)=int_(0)^(x)f(t)dt. Then the value of f(1n5) is

Let f:R to R be a function which satisfies f(x)=int_(0)^(x) f(t) dt .Then the value of f(In5), is

Let f: R rarr R be a continous function satisfying f(x) = x + int_(0)^(x) f(t) dt , for all x in R . Then the numbr of elements in the set S = {x in R: f (x) = 0} is -

Let f:R in R be a continuous function such that f(1)=2. If lim_(x to 1) int-(2)^(f(x)) (2t)/(x-1)dt=4 , then the value of f'(1) is

Let f(x) be an odd continuous function which is periodic with period 2. if g(x)=int_(0)^(x) f(t)dt , then

Let f be a continuous function on R and satisfies f(x)=e^(x)+int_(0)^(1)e^(x)f(t)dt, then which of the following is(are) correct?

A continuous function f(x) satisfies the relation f(x)=e^(x)+int_(0)^(1)e^(x)f(t)dt then f(1)=

let f:R rarr R be a continuous function defined by f(x)=(1)/(e^(x)+2e^(-x))

Let f:[0,oo)rarr R be a continuous strictly increasing function,such that f^(3)(x)=int_(0)^(x)t*f^(2)(t)dt for every x>=0. Then value of f(6) is

RESONANCE-DEFINITE INTEGRATION & ITS APPLICATION -Exercise 3 Part - I
  1. If I(n) = int(-x)^(x) (sinnx)/((1+pi^(x))sinx)dx, n = 0,1,2"……..", the...

    Text Solution

    |

  2. Let f : R rarr R be a continuous function function which satisfies f(x...

    Text Solution

    |

  3. The area of the region bounded by the curve y=e^x and lines x=0a n dy=...

    Text Solution

    |

  4. The value of lim(xrarr0)(1)/(x^(3))int(x)^(0) (tln(1+t))/(t^(4)+4) dt ...

    Text Solution

    |

  5. The value(s) of int(0)^(1) (x^(4)(1-x)^(4))/(1+x^(2))dx is are

    Text Solution

    |

  6. Let f be a real-valued function defined on the interval (0,oo) by f(x)...

    Text Solution

    |

  7. For any real number, let [x] denotes the largest integer less than or ...

    Text Solution

    |

  8. Let f be a real-valued function defined on the interval (-1,1) such th...

    Text Solution

    |

  9. Consider the polynomial f(x)= 1+2x+3x^2+4x^3. Let s be the sum of all ...

    Text Solution

    |

  10. Consider the polynomial f(x)= 1+2x+3x^2+4x^3. Let s be the sum of all ...

    Text Solution

    |

  11. Consider the polynomial f(x)= 1+2x+3x^2+4x^3. Let s be the sum of all ...

    Text Solution

    |

  12. The value of int(sqrt(ln2))^(ln3)(xsinx^(2))/(sinx^(2)+sin(ln6-x^(2)))...

    Text Solution

    |

  13. Let the straight line x = b divide the area enclosed by y = (1-x)^(2),...

    Text Solution

    |

  14. Let f : [-1,2]rarr[0,oo) be a continuous function such that f(x) = f(1...

    Text Solution

    |

  15. Let S be the area of the region enclosed by y=e^-x^2,y=0,x=0,a n dx=1....

    Text Solution

    |

  16. The value of the integral int(-pi//2)^(pi//2) (x^(2)+ln'(pi+x)/(x-a)) ...

    Text Solution

    |

  17. Let f(x) = (1-x)^(2) sin^(2)x+ x^(2) for all x in IR and let g(x) = in...

    Text Solution

    |

  18. Let f(x) = (1-x)^(2) sin^(2)x+ x^(2) for all x in IR and let g(x) = in...

    Text Solution

    |

  19. If f(x) = int(0)^(x) e^(t^(2)) (t-2) (t-3) dt for all x in (0, oo) , t...

    Text Solution

    |

  20. The area enclosed by the curvesy= sinx+cosx and y = | cosx-sin x | ove...

    Text Solution

    |