Home
Class 12
MATHS
If F(x)=int(1)^(x) f(t) dt,where f(t)=in...

If `F(x)=int_(1)^(x) f(t) dt`,where `f(t)=int_(1)^(t^(2))(sqrt(1+u^(4)))/(u) du`, then the value of F''(2) equals to

A

`(7)/(4sqrt17`

B

`(15)/(sqrt17)`

C

`sqrt(257)`

D

`(15sqrt17)/(68)`

Text Solution

Verified by Experts

The correct Answer is:
C
Promotional Banner

Topper's Solved these Questions

  • DEFINITE INTEGRAL

    ARIHANT MATHS|Exercise Exercise For Session 1|15 Videos

  • DEFINITE INTEGRAL

    ARIHANT MATHS|Exercise Exercise For Session 2|14 Videos

  • COORDINATE SYSTEM AND COORDINATES

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

  • DETERMINANTS

    ARIHANT MATHS|Exercise Exercise (Questions Asked In Previous 13 Years Exam)|18 Videos

Similar Questions

Explore conceptually related problems

If f(x)=int_(1)^(x)(ln t)/(1+t)dt, then

If f(x)=x+int_(0)^(1)t(x+t)f(t)dt, then the value of (23)/(2)f(0) is equal to

If int_(0)^(x^(2)) sqrt(1=t^(2)) dt, then f'(x)n equals

If int_(0)^(x^(2)(1+x))f(t)dt=x , then the value of f(2) is.

If int_(0)^(x^(2)(1+x))f(t)dt=x , then the value of 25f(2) must be_________.

If f:R in R is continuous and differentiable function such that int_(-1)^(x) f(t)dt+f'''(3) int_(x)^(1) dt=int_(1)^(x) t^(3)dt-f'(1)int_(0)^(x) t^(2)dt+f'(2) int_(x)^(3) r dt , then the value of f'(4), is

If f(x)=int_(0)^(x){f(t)}^(-1)dt and int_(0)^(1){f(t)}^(-1)=sqrt(2)

If F(x)=int_(1)^(x)(ln t)/(1+t+t^(2))dt then F(x)=-F((1)/(x))

f(x) = int_(x)^(x^(2))(e^(t))/(t)dt , then f'(t) is equal to :

ARIHANT MATHS-DEFINITE INTEGRAL-Exercise (Questions Asked In Previous 13 Years Exam)
  1. If F(x)=int(1)^(x) f(t) dt,where f(t)=int(1)^(t^(2))(sqrt(1+u^(4)))/(u...

    Text Solution

    |

  2. The value of int(-pi//2)^(pi//2) (x^(2)cos x )/(1+e^(x)) dx is equal ...

    Text Solution

    |

  3. The total number for distinct x epsilon[0,1] for which int(0)^(x)(t^(2...

    Text Solution

    |

  4. Let f(x)=7 tan^(8) x +7 tan^(6) x-3 tan^(4) x-3 tan^(2)x for all x in...

    Text Solution

    |

  5. Let f prime(x)=(192x^3)/(2+sin^4 pix) for all x in RR with f(1/2)=0. I...

    Text Solution

    |

  6. The option(s) with the values of aa n dL that satisfy the following eq...

    Text Solution

    |

  7. Let F:R- R be a thrice differentiable function. Suppose that F(1)=0,F(...

    Text Solution

    |

  8. Let F : R to R be a thrice differentiable function . Suppose that F(...

    Text Solution

    |

  9. Let f: RvecR be a function defined by f(x)={[x],xlt=2 0,x >2 where [...

    Text Solution

    |

  10. If alpha=int0^1(e^9x+3tan^((-1)x))((12+9x^2)/(1+x^2))dxw h e r etan^(-...

    Text Solution

    |

  11. The integral overset(pi//2)underset(pi//4)int (2 cosecx)^(17)dx is equ...

    Text Solution

    |

  12. Let f:[0,2]vecR be a function which is continuous on [0,2] and is diff...

    Text Solution

    |

  13. Match the conditions/ expressions in Column I with statement in Column...

    Text Solution

    |

  14. Match List I with List II and select the correct answer using codes gi...

    Text Solution

    |

  15. The value of int0^1 4x^3{(d^2)/(dx^2)(1-x^2)^5}dxi s

    Text Solution

    |

  16. The value of the integral int(-pi//2)^(pi//2) (x^(2) + log" (pi-x)/(pi...

    Text Solution

    |

  17. The value of int(sqrt(ln2))^(sqrt(ln3)) (xsinx^2)/(sinx^2+sin(ln6-x^2)...

    Text Solution

    |

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

    Text Solution

    |

  19. The value of int(0)^(1) (x^(4)(1-x)^(4))/(1+x^(2)) dx is (are)

    Text Solution

    |

  20. For a in R ( the set of all real number) , a ne -1, lim(n to oo)((1^...

    Text Solution

    |

  21. Consider the statements : P : There exists some x IR such that f(x)...

    Text Solution

    |