Home
Class 12
MATHS
If f(x)= int(0)^(x)(f(t))^(2) dt, f:R ra...

If `f(x)= int_(0)^(x)(f(t))^(2) dt, f:R rarr R ` be differentiable function and `f(g(x))` is differentiable at `x=a`, then

A

g (x) must be differentiable at `x=a`

B

g(x) may be non-differentiable at `x=a`

C

g(x) may be discontinous at `x=a`

D

None of the above

Text Solution

Verified by Experts

The correct Answer is:
A
Promotional Banner

Topper's Solved these Questions

  • DEFINITE INTEGRAL

    ARIHANT MATHS|Exercise Exercise (More Than One Correct Option Type Questions)|10 Videos

  • DEFINITE INTEGRAL

    ARIHANT MATHS|Exercise Exercise (Passage Based Questions)|17 Videos

  • DEFINITE INTEGRAL

    ARIHANT MATHS|Exercise Exercise For Session 6|10 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:R rarr R is a differentiable function such that f(x)>2f(x) for all x in R and f(0)=1, then

f(x)=int_0^x e^t f(t)dt+e^x , f(x) is a differentiable function on x in R then f(x)=

if f:R rarr R is a differentiable function such that f'(x)>2f(x) for all x varepsilon R, and f(0)=1, then

Let f:R rarr R be a differential function satisfy f(x)=f(x-y)f(y)AA x,y in R and f'(0)=a,f'(2)=b then f'(-2)=

If :R rarr R^(+) be a differentiable function and g(x)=e^(2x)(2f(x)-3(f(x))^(2)+2(f(x))^(3))f or x in R ,then

If f:R rarr R be a differentiable function such that f(x+2y)=f(x)+f(2y)+4xy, AA x,y in R , f(2)=10 , then f(3)=?

Let f : (a, b) to R be twice differentiable function such that f(x) = int _(a) ^(x) g (t) dt for a differentiable function g(x) . If f(x) = 0 has exactly five distinct roots in (a,b) , then g(x) g'(x) = 0 has at least

A function f(x) is differentiable at x=c(c in R). Let g(x)=|f(x)|,f(c)=0 then

Let f:R rarr R satisfying |f(x)|<=x^(2),AA x in R be differentiable at x=0. Then find f'(0)

if f be a differentiable function such that f(x) =x^(2)int_(0)^(x)e^(-t)f(x-t). dt. Then f(x) =

ARIHANT MATHS-DEFINITE INTEGRAL-Exercise (Single Option Correct Type Questions)
  1. For f(x) =x^(4) +|x|, let I(1)= int (0)^(pi)f(cos x) dx and I(2)= int(...

    Text Solution

    |

  2. Let f be a positive function. If I1 = int(1-k)^k x f[x(1-x)]\ dx and I...

    Text Solution

    |

  3. Suppose that the quadratic function f(x) = ax^(2) + bx +c is non-negat...

    Text Solution

    |

  4. Let I (a) =int(0)^(pi) ((x)/(a)+ a sin x)^(2) dx, where 'a' is positiv...

    Text Solution

    |

  5. The set of value of 'a' which satisfy the equation int0^2(t-log2a)dt...

    Text Solution

    |

  6. lim(x rarr infty) (x^(3) int(-1//x)^(1//x)("In" (1+t^(2)))/(1+e^(t)) d...

    Text Solution

    |

  7. The value of sqrt(pi(int(0)^(2008)x| sinpi x| dx)) is equal to

    Text Solution

    |

  8. lim(n rarr infty) sum(k=1)^(n) (n)/(n^(2)+k^(2)x^(2)),x gt 0 is equa...

    Text Solution

    |

  9. Let a gt 0 and f(x) is monotonic increase such that f(0)=0 and f(a)=b...

    Text Solution

    |

  10. int(-1/sqrt3)^(-1/sqrt3)(x^4)/(1-x^4)cos^(- 1)((2x)/(1+x^2))dx

    Text Solution

    |

  11. int(0)^(infty)f(x+(1)/(x)). (In x )/(x)dx is equal to

    Text Solution

    |

  12. lim(lamda to 0)(int(0)^(1) (1+x)^(lambda ) dx)^(1//lambda) Is equal t...

    Text Solution

    |

  13. If g(x) is the inverse of f(x) and f(x) has domain x in [1,5], where...

    Text Solution

    |

  14. The value of the definite integral int(0)^(pi//2)sin x sin 2x sin 3x d...

    Text Solution

    |

  15. If f(x)= int(0)^(x)(f(t))^(2) dt, f:R rarr R be differentiable functi...

    Text Solution

    |

  16. The number of integral solutions of the equation 4int (0)^( infty)(In"...

    Text Solution

    |

  17. int(0)^(16n^(2)//pi) "cos" (pi)/(2)[(xpi)/(n)] dx is equal to

    Text Solution

    |

  18. If int-2^-1 (ax^2-5)dx=0 and 5 + int1^2 (bx + c) dx = 0, then

    Text Solution

    |

  19. The value of int(3)^(6)(sqrt(x+sqrt(12x-36))+sqrt(x-sqrt(12x- 36)))dx...

    Text Solution

    |

  20. Let In=int(-n)^n({x+1}*{x^2+2}+{x^2+2}{x^3+4})dx, where {*} denotet th...

    Text Solution

    |