Home
Class 12
MATHS
If f is continuous function and F(x)=int...

If `f` is continuous function and `F(x)=int_0^x((2t+3)dotint_t^2f(u)d u)dt ,` then `|(F^(2))/(f(2))|` is equal to_____

Text Solution

Verified by Experts

The correct Answer is:
7
`F'(x)=(2x+3)int_(x)^(2)f(u)du`
`:.F''(x)=-(2x+3)f(x)+(int_(x)^(2)f(u)du).2`
`F''(2)=-7f(2)+0`
Promotional Banner

Topper's Solved these Questions

  • DEFINITE INTEGRATION

    CENGAGE|Exercise JEE Main Previous Year|12 Videos

  • DEFINITE INTEGRATION

    CENGAGE|Exercise JEE Advanced Previous Year|38 Videos

  • DEFINITE INTEGRATION

    CENGAGE|Exercise Exercise (Matrix)|6 Videos

  • CURVE TRACING

    CENGAGE|Exercise Exercise|24 Videos

  • DETERMINANT

    CENGAGE|Exercise Multiple Correct Answer|5 Videos

Similar Questions

Explore conceptually related problems

If int_(0)^(x) f(t)dt=x^2+int_(x)^(1) t^2f(t)dt , then f'(1/2) is

Iff(x)=x+int_0^1t(x+t)f(t)dt ,t h e nt h ev a l u eof(23)/2f(0) is equal to _________

Let f be continuous and the function g is defined as g(x)=int_0^x(t^2int_0^tf(u)du)dt where f(1) = 3 . then the value of g' (1) +g''(1) is

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

Let f: R->R be a continuous function and f(x)=f(2x) is true AAx in Rdot If f(1)=3, then the value of int_(-1)^1f(f(x))dx is equal to (a)6 (b) 0 (c) 3f(3) (d) 2f(0)

Let f(x)=1/x^2 int_0^x (4t^2-2f'(t))dt then find f'(4)

Find the points of minima for f(x)=int_0^x t(t-1)(t-2)dt

Let f be a continuous function on [a , b]dot If F(x)=(int_a^xf(t)dt-int_x^bf(t)dt)(2x-(a+b)), then prove that there exist some c in (a , b) such that int_a^cf(t)dt-int_c^bf(t)dt=f(c)(a+b-2c)dot

If f' is a differentiable function satisfying f(x)=int_(0)^(x)sqrt(1-f^(2)(t))dt+1/2 then the value of f(pi) is equal to

CENGAGE-DEFINITE INTEGRATION -Exercise (Numerical)
  1. The value of int(0)^(1)(tan^(-1)x)/(cot^(-1)(1-x+x^(2))dx is.

    Text Solution

    |

  2. Let f(x) be differentiate function symmetric about x=2, then the value...

    Text Solution

    |

  3. Let f:[0,oo)vecR be a continuous strictly increasing function, such th...

    Text Solution

    |

  4. If f is continuous function and F(x)=int0^x((2t+3)dotintt^2f(u)d u)dt ...

    Text Solution

    |

  5. If the value of the definite integral int0^1(sin^(-1)sqrt(x))/(x^2-x+1...

    Text Solution

    |

  6. about to only mathematics

    Text Solution

    |

  7. Let g(x) be differentiable on R and int(sint)^1x^2g(x)dx=(1-sint), wh...

    Text Solution

    |

  8. If int0^oox^(2n+1)dote^(-xdx)=360 , then the value of n is

    Text Solution

    |

  9. Let f(x) be a derivable function satisfying f(x)=int0^x e^tsin(x-t)dt...

    Text Solution

    |

  10. Let f(x)=1/x^2 int0^x (4t^2-2f'(t))dt then find f'(4)

    Text Solution

    |

  11. If the value of the definite integral int0^1^(2007)C7x^(2000)dot(1-x)^...

    Text Solution

    |

  12. IfIn=int0^1(1-x^5)^n dx ,t h e n(55)/7(I(10))/(I(11))i se q u a lto

    Text Solution

    |

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

    Text Solution

    |

  14. L e tJ=int(-5)^(-4)(3-x^2)tan(3-x^2)dxa n dK=int(-2)^(-1)(6-6x+x^2) t...

    Text Solution

    |

  15. The value of the definite integral int(2-1)^(sqrt(2)+1)(x^4+x^2+2)/((x...

    Text Solution

    |

  16. Consider a real valued continuous function f such that f(x)=sinx + int...

    Text Solution

    |

  17. Iff(x)=x+int0^1t(x+t)f(t)dt ,t h e nt h ev a l u eof(23)/2f(0) is ...

    Text Solution

    |

  18. Let y=f(x)=4x^(3)+2x-6, then the value of int(0)^(2)f(x)dx+int(0)^(30)...

    Text Solution

    |

  19. The value of int(1)^(3)(sqrt(1+(x-1)^(3))+(x^(2)-1)^(1/3)+1)dx is .

    Text Solution

    |

  20. The value of int(0)^(1)xcos^(-1)((1-x^2)/(1+x^2)) dx (x>0) is equal to...

    Text Solution

    |