Home
Class 12
MATHS
f(x)=int0^x f(t) dt=x+intx^1 tf(t)dt, th...

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

A

`(1)/(2)`

B

0

C

1

D

`-(1)/(2)`

Text Solution

Verified by Experts

The correct Answer is:
A
Promotional Banner

Topper's Solved these Questions

  • INTEGRAL CALCULUS - 2

    VMC MODULES ENGLISH|Exercise JEE Main (Archive)|64 Videos

  • FUNCTIONS

    VMC MODULES ENGLISH|Exercise JEE Main & Advanced|8 Videos

  • INTEGRAL CALCULUS-1

    VMC MODULES ENGLISH|Exercise JEE ADVANCED (ARCHIVE)|25 Videos

Similar Questions

Explore conceptually related problems

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

If f(x)=1+1/x int_1^x f(t) dt, then the value of f(e^-1) is

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

If f(x)=int_0^x tf(t)dt+2, then

If int_(0)^(x^(2)(1+x))f(t)dt=x , then the value of f(2) is.

If f:R in R is continuous and differentiable function such that int_(-1)^(x) f(t)dt+f'''(3) int_(x)^(0) dt=int_(1)^(x) t^(3)dt-f'(1)int_(0)^(x) t^(2)dt+f'(2) int_(x)^(3) r dt , then the value of f'(4), is

If f(x)=x+int_0^1t(x+t)f(t) dt ,then the value of 23/2f(0) is equal to _________

If f(x) is a continuous function such that f(x) gt 0 for all x gt 0 and (f(x))^(2020)=1+int_(0)^(x) f(t) dt , then the value of {f(2020)}^(2019) is equal to

If f (x) =int _(0)^(g(x))(dt)/(sqrt(1+t ^(3))),g (x) = int _(0)^(cos x ) (1+ sint ) ^(2) dt, then the value of f'((pi)/(2)) is equal to:

If f (x) =int _(0)^(g(x))(dt)/(sqrt(1+t ^(3))),g (x) = int _(0)^(cos x ) (1+ sint ) ^(2) dt, then the value of f'((pi)/(2)) is equal to:

VMC MODULES ENGLISH-INTEGRAL CALCULUS - 2 -JEE Advanced (Archive)
  1. Let f:[0,2]vecR be a function which is continuous on [0,2] and is diff...

    Text Solution

    |

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

    Text Solution

    |

  3. f(x)=int0^x f(t) dt=x+intx^1 tf(t)dt, then the value of f(1) is

    Text Solution

    |

  4. Let f : R to R be a differentiable function and f(1) = 4. Then, the va...

    Text Solution

    |

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

    Text Solution

    |

  6. Let f (x)= int (x^(2))^(x ^(3))(dt)/(ln t) for x gt 1 and g (x) = in...

    Text Solution

    |

  7. Let f(x)=|secxcosx s e c^2x+cotx cos e c\ x cos^2x cos^2x cos e c^2x1c...

    Text Solution

    |

  8. For x >0,l e tf(x)=int1^x((log)e t)/(1+t)dtdot Find the function...

    Text Solution

    |

  9. Let a+b=4,w h e r ea<2,a n dl e tg(x) be a differentiable function. If...

    Text Solution

    |

  10. Determine a positive integer nlt=5 such that int0^1e^x(x-1)^n=16-6e

    Text Solution

    |

  11. about to only mathematics

    Text Solution

    |

  12. Investigate for the maxima and minima of the function f(x)=int1^x[2(t...

    Text Solution

    |

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

    Text Solution

    |

  14. Let S(n)=underset(k=1)overset(n)sum (n)/(n^(2)+nk+k^(2)) and T(n)=unde...

    Text Solution

    |

  15. Show that ("lim")(n vec oo)(1/(n+1)+1/(n+2)++1/(6n))=log6

    Text Solution

    |

  16. about to only mathematics

    Text Solution

    |

  17. about to only mathematics

    Text Solution

    |

  18. about to only mathematics

    Text Solution

    |

  19. Let O(0,0),A(2,0),a n dB(1 1/(sqrt(3))) be the vertices of a triangle....

    Text Solution

    |

  20. Consider the function defined implicitly by the equation y^3-3y+x=0 on...

    Text Solution

    |