Home
Class 12
MATHS
Let f(x), xge0, be a non-negative contin...

Let `f(x), xge0`, be a non-negative continous function,and let `F(x) = int_(0)^(x)f(t)dt, xge0`, if for some `cgt0,f(x)lec F(x)` for all `xge0`, then show that `f(x)=0` for all `xge0`.

Promotional Banner

Topper's Solved these Questions

  • DIFFERENT PRODUCTS OF VECTORS AND THEIR GEOMETRICAL APPLICATIONS

    CENGAGE PUBLICATION|Exercise Multiple correct answers type|11 Videos
  • DIFFERENTIATION

    CENGAGE PUBLICATION|Exercise Archives|14 Videos

Similar Questions

Explore conceptually related problems

If f(t) is an odd function, then int_(0)^(x)f(t) dt is -

Let f(x),xgeq0, be a non-negative continuous function. If f^(prime)(x)cosxlt=f(x)sinxAAxgeq0, then find f((5pi)/3)

If f(x)=int_(-1)^(x)|t|dt , then for any xge0,f(x) equals

f: R to R is a continuous and f(x)=int_(0)^(x)f(t)dt then f(log_(e)5)= ?

Let f be an odd continous function which is periodic with priod 2 if g(x) = int_0^x f(t) dt then

If f(x)=int_0^x(sint)/t dt ,x >0, then

Let f:RtoR be a continuous function which satisfies f(x)=int_(0)^(x)f(t)dt . Then the value of f(log_(e)5) is

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

For function f(x) = xcosfrac(1)(x),xge 1

Let f(x) be a differentiable function such that f(x)=x^2 +int_0^x e^-t f(x-t) dt then int_0^1 f(x) dx=

CENGAGE PUBLICATION-DIFFERENTIAL EQUATIONS-All Questions
  1. Each question contains statements given in two columns which have to b...

    Text Solution

    |

  2. Determine the equation of the curve passing through the origin, in ...

    Text Solution

    |

  3. Let f(x), xge0, be a non-negative continous function,and let F(x) = in...

    Text Solution

    |

  4. A hemi-spherical tank of radius 2 m is initially full of water and h...

    Text Solution

    |

  5. A curve C has the property that if the tangent drawn at any point P...

    Text Solution

    |

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

    Text Solution

    |

  7. Integrating factor of differential equation cosx(dy)/(dx)+ysinx=1 is

    Text Solution

    |

  8. Solution of the equation cos^2x(dy)/(dx)-(tan2x)y=cos^4x, where |x|< ...

    Text Solution

    |

  9. If integrating factor of x(1-x^2)dy+(2x^2y-y-a x^3)dx=0 is e^(intp ...

    Text Solution

    |

  10. A function y=f(x) satisfies (x+1)f^(prime)(x)-2(x^2+x)f(x)=((e^x)^2)/...

    Text Solution

    |

  11. The general solution of the differential equation, y^(prime)+yphi^(...

    Text Solution

    |

  12. The solution of (dy)/(dx)=(x^2+y^2+1)/(2x y) satisfying y(1)=1 is gi...

    Text Solution

    |

  13. The integrating factor of the differential equation (dy)/(dx)(x(log...

    Text Solution

    |

  14. The solution of the differential equation x(x^2+1)((dy)/(dx))=y(1-x^2)...

    Text Solution

    |

  15. The solution of the differential equation (dy)/(dx)=1/(x y[x^2siny^2+...

    Text Solution

    |

  16. The general solution of the equation (dy)/(dx)=1+x y is

    Text Solution

    |

  17. A normal is drawn at a point P(x , y) of a curve. It meets the x-ax...

    Text Solution

    |

  18. If the solution of the differential equation (dy)/(dx)-y=1-e^(-x) and...

    Text Solution

    |

  19. Let y=y(t) be a solution to the differential equation y^(prime)+2t y...

    Text Solution

    |

  20. If the dependent variable y is changed to z by the substitution ...

    Text Solution

    |