Home
Class 12
MATHS
The function f(x)= int0^x sqrt(1-t^4)dt ...

The function `f(x)= int_0^x sqrt(1-t^4)dt` is such that: (A) `t` is defined in the interval `[-1,1]` (B) `f(x)` is increasing dunction (C) f is an odd function (D) the point `(0,0)` is the point of inflexion

A

it is defined on the interval [-1,1]

B

it is an increasing function

C

it is an odd function

D

the point (0,0) is the point of inflection

Text Solution

Verified by Experts

Promotional Banner

Topper's Solved these Questions

  • MONOTONICITY MAXIMA AND MINIMA

    ARIHANT MATHS|Exercise EXAMPLE|6 Videos

  • MONOTONICITY MAXIMA AND MINIMA

    ARIHANT MATHS|Exercise Exercise For Session 1|7 Videos

  • MATRICES

    ARIHANT MATHS|Exercise Exercise (Questions Asked In Previous 13 Years Exam)|49 Videos

  • PAIR OF STRAIGHT LINES

    ARIHANT MATHS|Exercise Exercise (Questions Asked In Previous 13 Years Exam)|2 Videos

Similar Questions

Explore conceptually related problems

The function f(x)=int_(0)^(x)sqrt(1-t^(4))dt is such that: ( A) t is defined in the interval [-1,1] (B) f(x) is increasing dunction (C) fis an odd function (D) the point (0,0) is the point of inflexion

For the function f(x)=int_(0)^(x)(sin t)/(t)dt where x>0

Statement I The function f(x) = int_(0)^(x) sqrt(1+t^(2) dt ) is an odd function and g(x)=f'(x) is an even function , then f(x) is an odd function.

If f(t) is an odd function,then varphi(x)=int_(a)^(x)f(t)dt is an even function.

The function f(x)=int_(0)^(x) log _(|sin t|)(sin t + (1)/(2)) dt , where x in (0,2pi) , then f(x) strictly increases in the interval

A function f is defined by f(x)=\ int_0^picostcos(x-t)dt ,\ 0lt=xlt=2pi then find its minimum value.

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)=

STATEMENT 1:int_(a)^(x)f(t)dt is an even function if f(x) is an odd function.STATEMENT 2:int_(a)^(x)f(t)dx is an odd function if f(x) is an even function.

The interval in which the function f(x)=int_(0)^(x) ((t)/(t+2)-1/t)dt will be non- increasing is

ARIHANT MATHS-MONOTONICITY MAXIMA AND MINIMA-Exercise (Questions Asked In Previous 13 Years Exam)
  1. The function f(x)= int0^x sqrt(1-t^4)dt is such that: (A) t is defi...

    Text Solution

    |

  2. The least value of alpha in R for which 4alphax^(2)+(1)/(x)ge1, for al...

    Text Solution

    |

  3. The number of points in (-oo,oo) for which x^(2)-xsinx-cosx=0, is

    Text Solution

    |

  4. Let f : R ->(0,oo) and g : R -> R be twice differentiable functions...

    Text Solution

    |

  5. Let f:(0,oo) in R be given f(x)=overset(x)underset(1//x)int e^-(t+(1...

    Text Solution

    |

  6. The fuction f(x)=2|x|+|x+2|-||x+2|-2|x|} has a local minimum or a loca...

    Text Solution

    |

  7. A rectagular sheet of fixed permeter with sides having thir lengths in...

    Text Solution

    |

  8. A vertical line passing through the point (h, 0) intersects the ellips...

    Text Solution

    |

  9. Let f,g and h be real-valued functions defined on the interval [0,1] b...

    Text Solution

    |

  10. e total number of local maxima and local minima of the function f(x) =...

    Text Solution

    |

  11. If the function g:(-oo,oo)->(-pi/2,pi/2) is given by g(u)=2tan^-1(e^u)...

    Text Solution

    |

  12. The second degree polynomial f(x), satisfying f(0)=o, f(1)=1,f'(x)gt...

    Text Solution

    |

  13. If f(x)=x^(3)+bx^(2)+cx+dand 0 ltb^(2)ltc, then in (-oo,oo)

    Text Solution

    |

  14. If f(x)=x^(2)+2bx+2c^(2)and g(x)=-x^(2)-2cx+b^(2), such that minf(x)gt...

    Text Solution

    |

  15. The length of a longest interval in which the function 3sinx-4sin^(3...

    Text Solution

    |

  16. If f(x)=e^(1-x) then f(x) is

    Text Solution

    |

  17. The maximum value of (cosalpha(1))-(cos alpha(2))...(cosalpha(n)), u...

    Text Solution

    |

  18. If f(x) = {{:(e ^(x),,"," 0 le x lt 1 ,, ""), (2- e^(x - 1),,"," 1 lt ...

    Text Solution

    |

  19. If f(x) is a cubic polynomil which as local maximum at x=-1 . If f(2)=...

    Text Solution

    |

  20. Consider the function f:(-oo, oo) -> (-oo ,oo) defined by f(x) =(x^2...

    Text Solution

    |

  21. Consider the function f:(-oo, oo) -> (-oo ,oo) defined by f(x) =(x^2...

    Text Solution

    |