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

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

Text Solution

Verified by Experts

The correct Answer is:
6
Promotional Banner

Topper's Solved these Questions

  • INTEGRAL CALCULUS - 2

    VMC MODULES ENGLISH|Exercise JEE Main (Archive)|64 Videos

  • FUNCTIONS

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

  • INTEGRAL CALCULUS-1

    VMC MODULES ENGLISH|Exercise JEE ADVANCED (ARCHIVE)|25 Videos

Similar Questions

Explore conceptually related problems

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

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

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: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

VMC MODULES ENGLISH-INTEGRAL CALCULUS - 2 -JEE Advanced (Archive)
  1. The value of int(0)^(1)(x^(4)(1-x)^(4))/(1+x^(4))dx is (are)

    Text Solution

    |

  2. If int(n)=int(-pi)^(pi)(sin nx)/((1+pi^(x))sinx) dx, n=0,1,2,………. then

    Text Solution

    |

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

    Text Solution

    |

  4. Let d/(dx)F(x)=(e^(sinx))/x . x lt0. If int(1)^(4)(2e^(sinx^(2)))/xdx=...

    Text Solution

    |

  5. int(1)^(e^(37))(pisin(pilogx))/(x)dx equals to.

    Text Solution

    |

  6. Prove that: int0^(2pi)(xsin^(2n)x)/(sin^(2n)+cos^(2n)x)dx

    Text Solution

    |

  7. The value of int2^3(sqrt(x))/(sqrt(5-x)+sqrt(x))dxi s

    Text Solution

    |

  8. The value of overset(3pi//4)underset(pi//4)int (x)/(1+sin x) dx is equ...

    Text Solution

    |

  9. The value of int(-2)^2|1-x^2|dx is

    Text Solution

    |

  10. The integral int0^(1. 5)[x^2]dx ,w h e r e[dot] denotoes the greatest ...

    Text Solution

    |

  11. Match the conditions // expression in Column I with statement in Colum...

    Text Solution

    |

  12. Match List I with List II and select the correct answer using the code...

    Text Solution

    |

  13. Evaluate: 5050(int0 1(1-x^(50))^(100)dx)/(int0 1(1-x^(50))^(101)dx)

    Text Solution

    |

  14. Evaluate: int0^pie^(|cosx|)(2s in(1/2cosx)+3cos(1/2cosx))sinxdxdot

    Text Solution

    |

  15. Find the value of int(-pi/3)^(pi/3)(pi+4x^3)/(2-cos(|x|pi/3))dx

    Text Solution

    |

  16. Show that: int0^(pi//2)f(sin2x)sinxdx=sqrt(2)int0^(pi//4)f(cos2x)co...

    Text Solution

    |

  17. int(-pi)^(pi) ( e^(sin x ))/( e^(sinx) + e^(-sinx))dx is equal to

    Text Solution

    |

  18. Prove that int(0)^(1)tan^(-1)(1/(1-x+x^(2)))dx=2int(0)^(1)tan^(-1)xdx....

    Text Solution

    |

  19. Evaluate int(0)^(pi//4) log (1+tan theta)d theta

    Text Solution

    |

  20. about to only mathematics

    Text Solution

    |