Home
Class 12
MATHS
Let f:[1,oo] be a differentiable func...

Let `f:[1,oo]` be a differentiable function such that `f(1)=2.` If `int_1^xf(t)dt=3xf(x)-x^3` for all `xgeq1,` then the value of `f(2)` is

Text Solution

Verified by Experts

The correct Answer is:
c
Promotional Banner

Topper's Solved these Questions

  • DEFINITE INTEGRAL

    ARIHANT MATHS|Exercise Exercise (Single Integer Answer Type Questions)|5 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:[1,oo] be a differentiable function such that f(1)=2. If 6int_(1)^(x)f(t)dt=3xf(x)-x^(3) for all x>=1, then the value of f(2) is

Let f[1, infty) to [2, infty) be a differentiable function such that f(1) =1/3 . If 6 int_(1)^(x) f(t) dt = 3x f(x) -x^(3) for all x ge 1 , then the value of 3f(2) is

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

Let f be a differentiabel function satisfying int_(1)^(f(x))f^(-1)(t)dt=(1)/(3)(x^((3)/(2))-8)AA x>0 and f(1)=0 Then the value of f(9) is

Let f be a differentiabel function satisfying int_(1)^(f(x))f^(-1)(t)dt=(1)/(3)(x^((3)/(2))-8)AA x>0 and f(1)=0, Then the value of f(9) is

Let f:R in R be a continuous function such that f(1)=2. If lim_(x to 1) int-(2)^(f(x)) (2t)/(x-1)dt=4 , then the value of f'(1) is

ARIHANT MATHS-DEFINITE INTEGRAL-Exercise (Questions Asked In Previous 13 Years Exam)
  1. The value of the integral int(-pi//2)^(pi//2) (x^(2) + log" (pi-x)/(pi...

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

  7. Which of the following is true?

    Text Solution

    |

  8. For any real number x ,l e t[x] denote the largest integer less than o...

    Text Solution

    |

  9. Let f be a non-negative function defined on the interval .[0,1].If int...

    Text Solution

    |

  10. If In=int(-pi)^(pi) \ (sinnx)/((1+pi^x) \ sinx) \ dx, n=0,1,2,...... t...

    Text Solution

    |

  11. Let Sn=sum(k=0)^n n/(n^2+k n+k^2) and Tn=sum(k=0)^(n-1)n/(n^2+k n+k...

    Text Solution

    |

  12. The Integral int(pi/4)^((3pi)/4)(dx)/(1+cosx) is equal to: ...

    Text Solution

    |

  13. Let In=int tan^n x dx, (n>1). If I4+I6=a tan^5 x + bx^5 + C, Where C...

    Text Solution

    |

  14. lim(n rarr infty ) [((n+1)(n+2)...3n)/(n^(2n))]^(1//n) is equal to

    Text Solution

    |

  15. The integral int2^4(logx^2)/(logx^2+log(36-12 x+x^2)dx is equal to:...

    Text Solution

    |

  16. The integral int(0)^(pi) sqrt(1+4 sin )(x)/(2) -4 "sin" (x)/(2) dx is...

    Text Solution

    |

  17. Statement I The value of the integral int(pi//6)^(pi//3) (dx)/(1+sqrt...

    Text Solution

    |

  18. The intercepts on x-axis made by tangents to the curve, y=int0^x|t|...

    Text Solution

    |

  19. Ifg(x)= int(0)^(x) cos ^(4)t dt, "then " g (x+pi) equals

    Text Solution

    |

  20. The value of int(0)^(1) (8 log(1+x))/(1+x^(2)) dx is

    Text Solution

    |