Home
Class 12
MATHS
Let f:[1,oo] be a differentiable funct...

Let `f:[1,oo]` be a differentiable function such that `f(1)=2.` If `6int_1^xf(t)dt=3xf(x)-x^3` for all `xgeq1,` then the value of `f(2)` is

Text Solution

AI Generated Solution

To solve the problem, we start with the given equation: \[ 6 \int_1^x f(t) \, dt = 3x f(x) - x^3 \] for all \( x \geq 1 \). ...
Promotional Banner

Topper's Solved these Questions

  • DIFFERENTIAL EQUATIONS

    CENGAGE ENGLISH|Exercise Archives|12 Videos

  • DIFFERENTIAL EQUATIONS

    CENGAGE ENGLISH|Exercise Jee advanced|3 Videos

  • DIFFERENTIAL EQUATIONS

    CENGAGE ENGLISH|Exercise Linked Comprehension types|21 Videos

  • DIFFERENT PRODUCTS OF VECTORS AND THEIR GEOMETRICAL APPLICATIONS

    CENGAGE ENGLISH|Exercise Multiple correct answers type|11 Videos

  • DIFFERENTIATION

    CENGAGE ENGLISH|Exercise Archives|14 Videos

Similar Questions

Explore conceptually related problems

Let f[1, infty) to [2, infty) be a differentiable function such that f(1) =1/3 . If 6 int_(1)^(x) f(t) dt = 3x f(x) -x^(3) for all x ge 1 , then the value of 3f(2) is

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=

Let f:(0,oo)->R be a differentiable function such that f'(x)=2-f(x)/x for all x in (0,oo) and f(1)=1 , then

Let f:(0,oo)->R be a differentiable function such that f'(x)=2-f(x)/x for all x in (0,oo) and f(1)=1 , then f(x) is

If f(x) is differentiable function such that int_0^xf(t)dt=((f(x))^2)/2 for all x and f(2)!=0, then value of f ' (2) is a. 3 b. 1 c. 2 d. -1 e. -2

Let f:[0,oo)->R be a continuous strictly increasing function, such that f^3(x)=int_0^x t*f^2(t)dt for every xgeq0. Then value of f(6) is_______

Let f:[0,oo) to R be a continuous strictly increasing function, such that f^3(x)=int_0^x tdotf^2(t)dt for every xgeq0. Then value of f(6) is_______

Let f(x) be a differentiable function such that int_(t)^(t^(2))xf(x)dx=(4)/(3)t^(3)-(4t)/(3)AA t ge0 , then f(1) is equal to

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

if f(x) is a differential function such that f(x)=int_(0)^(x)(1+2xf(t))dt&f(1)=e , then Q. int_(0)^(1)f(x)dx=

CENGAGE ENGLISH-DIFFERENTIAL EQUATIONS-Numerical value type
  1. If y=y(x) and it follows the relation 4x e^(x y)=y+5sin^2x , then ...

    Text Solution

    |

  2. If x(dy)/(x t)=x^2+y-2,y(1)=1, then y(2) equal

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

  5. If the solution of the differential equation (dy)/(dx)=1/(xcosy+sin2y)...

    Text Solution

    |

  6. If the independent variable x is changed to y , then the differe...

    Text Solution

    |

  7. Let y(1) and y(2) be two different solutions of the equation (dy)/(d...

    Text Solution

    |

  8. Tangent is drawn at the point (xi ,yi) on the curve y=f(x), which ...

    Text Solution

    |

  9. The perpendicular from the origin to the tangent at any point on a ...

    Text Solution

    |

  10. If the eccentricity of the curve for which tangent at point P inter...

    Text Solution

    |

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

    Text Solution

    |

  12. Let f be a function defined on the interval [0,2pi] such that int(0)^(...

    Text Solution

    |

  13. Let y(x) be a function satisfying d^(2)y//dx^(2)-dy//dx+e^(2x)=0,y(0)=...

    Text Solution

    |

  14. Let f be a real-valued differentiable function on R (the set of ...

    Text Solution

    |

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

    Text Solution

    |

  16. Let f:[1,oo] be a differentiable function such that f(1)=2. If 6int1...

    Text Solution

    |

  17. Let f:R to R be a differentiable function with f(0)=0. If y=f(x) satis...

    Text Solution

    |