Home
Class 12
MATHS
Let f: R to R be a continuous function w...

Let `f: R to R` be a continuous function which satisfies `f(x)=` `int_0^xf(t)dtdot` Then the value of `f(1n5)` is______

Text Solution

Verified by Experts

The correct Answer is:
0
Promotional Banner

Topper's Solved these Questions

  • DIFFERENTIAL EQUATIONS

    VMC MODULES ENGLISH|Exercise JEE MAIN (ARCHIVE )|28 Videos
  • DIFFERENTIAL CALCULUS 2

    VMC MODULES ENGLISH|Exercise JEE Advanced (Archive)|81 Videos
  • FUNCTIONS

    VMC MODULES ENGLISH|Exercise JEE Main & Advanced|8 Videos

Similar Questions

Explore conceptually related problems

A continuous function f(x) satisfies the relation f(x)=e^x+int_0^1 e^xf(t)dt then f(1)=

If int_0^xf(t) dt=x+int_x^1 tf(t)dt, then the value of f(1)

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 continuous functions f: RvecR satisfying f(0)=1a n df(2x)-f(x)=xdot Then the value of f(3) is 2 b. 3 c. 4 d. 5

Let f(x) be continuous functions f: RvecR satisfying f(0)=1a n df(2x)-f(x)=xdot Then the value of f(3) is 2 b. 3 c. 4 d. 5

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

Let: f:[0,3]vecR be a continuous function such that int_0^3f(x)dx=3. If I=int_0^3(xf(x)+int_0^xf(t)dt)dx , then value of I is equal to

Let f be a continuous function on R such that f (1/(4n))=sin e^n/(e^(n^2))+n^2/(n^2+1) Then the value of f(0) is

Let f be a continuous function on R such that f (1/(4n))=sin e^n/(e^(n^2))+n^2/(n^2+1) Then the value of f(0) is

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))

VMC MODULES ENGLISH-DIFFERENTIAL EQUATIONS-JEE ADVANCE (ARCHIVE )
  1. Let a solution y=y(x) of the differential equation xsqrt(x^(2)-1) dy-...

    Text Solution

    |

  2. Prove that for x in [0, (pi)/(2)], sin x + 2x ge (3x(x + 1))/(pi).

    Text Solution

    |

  3. Let f: R to R be a continuous function which satisfies f(x)= int0^xf(...

    Text Solution

    |

  4. Let f:[0,1]rarrR (the set of all real numbers) be a function. Suppose ...

    Text Solution

    |

  5. Let f:[0,1]rarrR (the set of all real numbers) be a function. Suppose ...

    Text Solution

    |

  6. Let f(x) = (1 - x)^2 sin^2 x + x^2 for all x ∈ R, and let g(x) = ∫((2...

    Text Solution

    |

  7. Consider the statements : P : There exists some x IR such that f(x)...

    Text Solution

    |

  8. The function y=f(x) is the solution of the differential equation (d...

    Text Solution

    |

  9. Let f:[1/2,1]->R (the set of all real numbers) be a positive, non-cons...

    Text Solution

    |

  10. Let the f (x) be differentiabe function on the interval (0,oo) such ...

    Text Solution

    |

  11. Integrating factor of sec^2y dy/dx+x tany=x^3

    Text Solution

    |

  12. Let u(x) and v(x) be two continous functions satisfying the different...

    Text Solution

    |

  13. Let y^(prime)(x)+y(x)g^(prime)(x)=g(x)g^(prime)(x),y(0),x in R , wher...

    Text Solution

    |

  14. A curve passes through the point (1,pi/6) . Let the slope of the curve...

    Text Solution

    |

  15. Tangent is drawn at any point P of a curve which passes through (1, 1...

    Text Solution

    |

  16. A spherical rain drop evaporates at a rate proportional to its surf...

    Text Solution

    |

  17. If length of tangent at any point on the curve y=f(x). Intercepted bet...

    Text Solution

    |

  18. A right circular cone with radius R and height H contains a liquid whi...

    Text Solution

    |

  19. A country has a food deficit of 10%. Its population grows continuously...

    Text Solution

    |

  20. A curve passing through the point (1,1) has the porperty that the perp...

    Text Solution

    |