Home
Class 12
MATHS
Let f : (0, oo) rarr R be a continuous f...

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

A

216

B

219

C

222

D

225

Text Solution

Verified by Experts

The correct Answer is:
B
Promotional Banner

Topper's Solved these Questions

  • CONTINUITY AND DIFFERENTIABILITY

    ARIHANT MATHS|Exercise Exercise (More Than One Correct Option Type Questions)|26 Videos
  • CONTINUITY AND DIFFERENTIABILITY

    ARIHANT MATHS|Exercise Exercise (Statement I And Ii Type Questions)|11 Videos
  • CONTINUITY AND DIFFERENTIABILITY

    ARIHANT MATHS|Exercise Exercise For Session 7|10 Videos
  • COMPLEX NUMBERS

    ARIHANT MATHS|Exercise Complex Number Exercise 8|3 Videos
  • COORDINATE SYSTEM AND COORDINATES

    ARIHANT MATHS|Exercise Exercise (Questions Asked In Previous 13 Years Exam)|7 Videos

Similar Questions

Explore conceptually related problems

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:R rarr R be a continuous function such that f(x)-2f(x/2)+f(x/4)=x^(2) . f'(0) is equal to

Let f:R rarr R be a continuous function such that f(x)-2f(x/2)+f(x/4)=x^(2) . f(3) is equal to

Let f:R to R be a differentiable function such that f(x)=x^(2)+int_(0)^(x)e^(-t)f(x-t)dt . f(x) increases for

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:R rarr R be a continuous function such that f(x)-2f(x/2)+f(x/4)=x^(2) . The equation f(x)-x-f(0)=0 have exactly

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=

ARIHANT MATHS-CONTINUITY AND DIFFERENTIABILITY-Exercise (Single Option Correct Type Questions)
  1. A derivable function f : R^(+) rarr R satisfies the condition f(x) - f...

    Text Solution

    |

  2. If (d(f(x)))/(dx) = e^(-x) f(x) + e^(x) f(-x), then f(x) is, (given f(...

    Text Solution

    |

  3. Let f : (0, oo) rarr R be a continuous function such that f(x) = int(0...

    Text Solution

    |

  4. For let h(x)={1/q if x=p/q and 0 if x is irrational where p & q ...

    Text Solution

    |

  5. Let f(x) = (g(x))/(h(x)), where g and h are continuous functions on th...

    Text Solution

    |

  6. Find dy/dx if y=2x^7

    Text Solution

    |

  7. if f(x) =(x-e^(x)+ cos 2x)/(x^(2)),xne0 , is continuous at x=0 , t...

    Text Solution

    |

  8. Consider the function f(x) = {{:(x{x}+1",","if",0 le x lt 1),(2-{x}","...

    Text Solution

    |

  9. Let f(x) = {{:((2^(x)+2^(3-x) - 6)/(sqrt(2^(-x))-2^(1-x))",","if",x gt...

    Text Solution

    |

  10. Let [x] denote the integral part of x in R and g(x) = x- [x]. Let f(x...

    Text Solution

    |

  11. Let f be a differentiable function on the open interval(a, b). Which o...

    Text Solution

    |

  12. Number of points where the function f(x)=(x^2-1)|x^2-x-2| + sin(|x|) i...

    Text Solution

    |

  13. Consider function f: R - {-1,1}-> R. f(x)=x/[1-|x|] Then the incorrect...

    Text Solution

    |

  14. Find dy/dx if 2y-e^x=6

    Text Solution

    |

  15. The total number of points of non-differentiability of f(x) = min[|sin...

    Text Solution

    |

  16. The function f(x)=[x]^2-[x^2] is discontinuous at (where [gamma] is t...

    Text Solution

    |

  17. The function f(x)=(x^2-1)|x^2-3x+2|+cos(|x|) is differentiable not dif...

    Text Solution

    |

  18. If f(x) = {{:((1)/(e^(1//x))",",x ne 0),(0",",x = 0):} then

    Text Solution

    |

  19. Given f(x) = (e^(x)-cos 2x - x)/(x^(2)),"for x" in R-{0} g(x) = {{:(f...

    Text Solution

    |

  20. The function g(x) = {{:(x+b",",x lt 0),(cos x",",x ge 0):} can be made...

    Text Solution

    |