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

Suppose f(x) and g(x) are two continuous function defined for 0 le xle 1 . Given , f(x)= int_(0)^(1) e^(x+1) . F(t) dt and g(x)=int _(0)^(1) e^(x+t). G(t) dt +x , The value of f(1) equals

If int_0^x f(t) dt=x+int_x^1 tf(t)dt, then the value of f(1) is

Suppose f(x) and g(x) are two continuous functions defined for 0<=x<=1 .Given, f(x)=int_0^1 e^(x+1) .f(t) dt and g(x)=int_0^1 e^(x+1) *g(t) dt+x The value of f( 1) equals

If f(x)=int_0^x{f(t)}^(- 1)dt and int_0^1{f(t)}^(- 1)=sqrt(2), then

Let f(x)=int_2^x (dt)/sqrt(1+t^4) and g be the inverse of f . Then, the value of g'(0) is

Let f(x)=int_(0)^(x)"cos" ((t^(2)+2t+1)/(5))dt,0>x>2, then

Let f: RvecR be a continuous odd function, which vanishes exactly at one point and f(1)=1/2dot Suppose that F(x)=int_(-1)^xf(t)dtfora l lx in [-1,2]a n dG(x)=int_(-1)^x t|f(f(t))|dt fora l lx in [-1,2]dot If (lim)_(x vec 1)(F(x))/(G(x))=1/(14), Then the value of f(1/2) is

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 total number of distinct x in R for which |{:(x,x^(2),1+x^(3)...

    Text Solution

    |

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

    Text Solution

    |

  4. Let f'(x)=(192x^(3))/(2+sin^(4)pix) for all x epsilonR with f(1/2)=0. ...

    Text Solution

    |

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

    Text Solution

    |

  6. Let F:RtoR be a thrice differntiable function. Suppose that F(1)=0,F(3...

    Text Solution

    |

  7. Let F:RtoR be a thrice differntiable function. Suppose that F(1)=0,F(3...

    Text Solution

    |

  8. If f(x)=x-[x], where [x] is the greatest integer less than or equal to...

    Text Solution

    |

  9. If alpha=int0^1(e^(9x+3tan^(-1)x))((12+9x^2)/(1+x^2))dx where tan^(-1)...

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

  13. Find x+y+z

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

  16. The value of int(In2)^(In3) (x sinx)dx is

    Text Solution

    |

  17. Let f:[1,oo] be a differentiable function such that f(1)=2. If 6int1...

    Text Solution

    |

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

    Text Solution

    |

  19. For a epsilonR (the set of all real numbers) a!=-1, lim(n to oo) ((1^...

    Text Solution

    |

  20. Let f:[0,1]toR (the set of all real numbers ) be a function. Suppose t...

    Text Solution

    |

  21. Which of the following is true?

    Text Solution

    |