Home
Class 12
MATHS
Let f:(0,oo)to R and F(x)=int(0)^(x) f(t...

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

A

`(5)/(4)`

B

7

C

4

D

2

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 6|10 Videos

  • DEFINITE INTEGRAL

    ARIHANT MATHS|Exercise Exercise (Single Option Correct Type Questions)|34 Videos

  • DEFINITE INTEGRAL

    ARIHANT MATHS|Exercise Exercise For Session 4|20 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

Let f:(0, oo) in R and F(x) = int_(0)^(x) f(t) dt . If F(x^(2))=x^(2)(1+x) then f (4) equals

Let f : (0,oo) to R and F(x)=int_(0)^(x)t f(t)dt . If F(x^(2))=x^(4)+x^(5) , then

Let f:(0, oo) rarr R and F(x^(2))=int_(0)^(x^(2))f(t)dt. " If "F(x^(2))=x^(2)(1+x) , then f(4) is equal to ________________

f:(0,oo)->R and F(x)=int_(0)^(x)f(t)dtIfF(x^(2))=x^(2)(1+x),thenf(4)

Let f:(0,oo)rarr R and 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)) equals (A) 216(B)219 (C) 221(D)225

Let f:(0,oo)rarr R and F(x^(3))=int_(0)^(x^(2))f(t)dt If F(x^(3))=x^(3)(x^(2)+x+1), then f(27)=

Let f:(0,oo)rarrR and F(x)=int_0^x f(t)dt . If F(x^2)=x^2(1+x) , then f(4)= (A) 5/4 (B) 7 (C) 4 (D) 2

Let f:(0,oo)to R be a continuous function such that F(x)=int_(0)^(x^(2)) tf(t)dt. "If "F(x^(2))=x^(4)+x^(5),"then "sum_(r=1)^(12) f(r^(2))=

ARIHANT MATHS-DEFINITE INTEGRAL-Exercise For Session 5
  1. The value of int-1^10 sgn (x -[x])dx is equal to (where, [:] denotes t...

    Text Solution

    |

  2. the value of int(0)^([x]) dx (where , [.] denotes the greatest integer...

    Text Solution

    |

  3. Evaluate: int(-pi/4)^(npi-pi/4)|sinx+cosx|dx

    Text Solution

    |

  4. Let f (x) = x – [x], for every real number x, where [x] is the greates...

    Text Solution

    |

  5. f(x)=int0^xf(t)dt=x+intx^1tf(t)dt ,t h e nt h ev a l u eoff(1)i s 1/2...

    Text Solution

    |

  6. The least value of the function phi(x)=overset(x)underset(5pi//4)int...

    Text Solution

    |

  7. The poins of extremum of phi(x)=underset(1)overset(x)inte^(-t^(2)//2)...

    Text Solution

    |

  8. If f(x) is periodic function with period, T, then

    Text Solution

    |

  9. Let d/(dx) (F(x))= e^(sinx)/x, x>0. If int1^4 2e^sin(x^2)/x dx = F(k)...

    Text Solution

    |

  10. Let f:(0,oo)to R and F(x)=int(0)^(x) f(t)dt. " If " F(x^(2))=x^(2)(1+x...

    Text Solution

    |

  11. Let T >0 be a fixed real number. Suppose f is continuous function such...

    Text Solution

    |

  12. Let f(x)=int1^xsqrt(2-t^2)dtdot Then the real roots of the equation , ...

    Text Solution

    |

  13. Let f(x) be an odd continuous function which is periodic with period...

    Text Solution

    |

  14. Let f(x) be a function defined by f(x)=int1^xt(t^2-3t+2)dt,1<=x<=3 The...

    Text Solution

    |

  15. The value of lim(x rarr0)(2int(0)^(cos x ) cos^(-1) (t))/(2x- sin 2 x)...

    Text Solution

    |

  16. If underset(0)overset(x)int (bt cos 4 t - a sin 4t)/( t^(2))dt=(a sin ...

    Text Solution

    |

  17. If f(x)=int0^x{f(t)}^(- 1)dt and int0^1{f(t)}^(- 1)=sqrt(2), then

    Text Solution

    |

  18. Let f be a real-valued function defined on the inverval (-1,1) such th...

    Text Solution

    |

  19. Concider the function defined on [0,1] rarr R f(x) =(sinx- cosx)/(x^(2...

    Text Solution

    |

  20. Concider the function defined on [0,1] rarr R f(x) =(sinx- cosx)/(x^(2...

    Text Solution

    |