Home
Class 12
MATHS
f:(0,infty)rarrR and F(x)=int(0)^(x)t f(...

`f:(0,infty)rarrR and F(x)=int_(0)^(x)t f(t)dt`
If `F(x^(2))=x^(4)+x^(5),"then" underset(r=1)overset(12)(Sigma)f(r^(2))` is equal to S

A

`216`

B

`219`

C

`221`

D

`225`

Text Solution

Verified by Experts

Promotional Banner

Topper's Solved these Questions

  • INTEGRALS

    AAKASH INSTITUTE ENGLISH|Exercise Objective Type Questions (More than one answer)|32 Videos
  • INTEGRALS

    AAKASH INSTITUTE ENGLISH|Exercise Linked Comprehension Type Questions|11 Videos
  • INTEGRALS

    AAKASH INSTITUTE ENGLISH|Exercise Competition level Questions|80 Videos
  • DIFFERENTIAL EQUATIONS

    AAKASH INSTITUTE ENGLISH|Exercise Assignment Section - J (Aakash Challengers Questions)|4 Videos
  • INVERSE TRIGONOMETRIC FUNCTIONS

    AAKASH INSTITUTE ENGLISH|Exercise ASSIGNMENT (SECTION - J)(ANKASH CHALLENGERS QUESTIONS)|4 Videos

Similar Questions

Explore conceptually related problems

Let f : (0,oo) to R and F(x)=int_(0)^(x)t f(t)dt . If F(x^(2))=x^(4)+x^(5) , then

f:(0,infty)rarrR and F(x)=int_(0)^(x)t f(t)dt If F(x^(2))=x^(4)+x^(5),"then" Sigma_(r=1)^(12)f(r^(2)) is equal to S

Let f : (0, oo) rarr R be a continuous function such that f(x) = int_(0)^(x) t f(t) dt . If f(x^(2)) = x^(4) + x^(5) , then sum_(r = 1)^(12) f(r^(2)) , is equal to

Let f:(0,oo)to R and F(x)=int_(0)^(x) f(t)dt. " If " F(x^(2))=x^(2)(1+x) , then f(4) equals

Let f:(0,oo)to R be a continuous function such that F(x)=int_(0)^(x^(2)) tf(t)dt. "If "F(x^(2))=x^(4)+x^(5),"then "sum_(r=1)^(12) f(r^(2))=

Let f: (0,oo)->R and F(x^3)=int_0^ 3f(t)dt, if F(x^3)=x^3(x^2+x+1) .Then f(27)=

If f(x)=x^(2)int_(0)^(1)f(t)dt+2 , then

If int_(0)^(x)f(t)dt = x^(2)-int_(0)^(x^(2))(f(t))/(t)dt then find f(1) .

If int_(0)^(x)f(t)dt=e^(x)-ae^(2x)int_(0)^(1)f(t)e^(-t)dt , then

" If " f(x) =int_(0)^(x)" t sin t dt tehn " f(x) is

AAKASH INSTITUTE ENGLISH-INTEGRALS-Objective Type Questions (Only one answer)
  1. Let f(x) be a function satisfyingf'(x)=f(x) withf(0) =1 and g(x) be a ...

    Text Solution

    |

  2. Suppose that F(x) is an anti-derivative of f(x)=(sinx)/x ,w h e r ex >...

    Text Solution

    |

  3. If f(x)=[{:(sqrt(1-x), , , 0 le x le 1),((7x-6)^(-1) , , ,1 le x le 2)...

    Text Solution

    |

  4. If f:RrarrR defined by f(x)=sinx+x, then find the value of int0^pi(f^-...

    Text Solution

    |

  5. The value of int0^100 [tan^-1 x]dx is, (where [*] denotes greatest in...

    Text Solution

    |

  6. Iff(x)={0,w h e r ex=n/(n+1),n=1,2,31,e l s e w h e r e t h e nt h ev...

    Text Solution

    |

  7. Let g(x) be a continous and differentiable function such that int(0...

    Text Solution

    |

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

    Text Solution

    |

  9. f:(0,infty)rarrR and F(x)=int(0)^(x)t f(t)dt If F(x^(2))=x^(4)+x^(5)...

    Text Solution

    |

  10. int(-pi//4) ^(pi//4) x^(3) sin^(4) xdx=

    Text Solution

    |

  11. The value of int(-10)^(10)[{f(f(x)}+{f(f((1)/(x))}]dx, where f(x)=(1-x...

    Text Solution

    |

  12. The value of int(-2)^(2)(ax^(2011)+bx^(2001)+c)dx, where a, b, c are c...

    Text Solution

    |

  13. If for non zero x, 3f(x)+4f((1)/(x))=(1)/(x)-10, then the value of int...

    Text Solution

    |

  14. The value of int(2010pi+(pi)/(6))^(2010pi+(pi)/(3))(sinx+cosx)dx is

    Text Solution

    |

  15. Let int(a)^(b)f(x)dx=int(a+c)^(b+c)f(x-c)dx. Then the value of int(0)^...

    Text Solution

    |

  16. If x^(f(x))=e^(x-f(x)), then the value of integral int(1)^(2)f'(x){(1+...

    Text Solution

    |

  17. If overset(x)underset(e )int t f(t)dt=sin x-x cos x-(x^(2))/(2) for al...

    Text Solution

    |

  18. The value of the integral int(-2012pi)^(2012pi) {d/dx(int0^(x^2) cost^...

    Text Solution

    |

  19. The value of int(-2010pi)^(2010pi) {x^2011(1+tan(pi/3-x)(1+tan(x-pi/1...

    Text Solution

    |

  20. Let f(x)=min{|x+2|,|x|,|x-2|} then the value of the integral int-2^2 ...

    Text Solution

    |