Home
Class 12
MATHS
Let f: R to R be a continuous function w...

Let `f: R to R` be a continuous function which satisfies `f(x)=` `int_0^xf(t)dtdot` Then the value of `f(1n5)` is______

Text Solution

Verified by Experts

The correct Answer is:
0
Promotional Banner

Topper's Solved these Questions

  • DEFINITE INTEGRAL

    ARIHANT MATHS|Exercise Exercise For Session 1|15 Videos

  • DEFINITE INTEGRAL

    ARIHANT MATHS|Exercise Exercise For Session 2|14 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: R to R be a continuous function which satisfies f(x)= int_0^xf(t)dtdot Then the value of f(1n6) is______

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

Let f be a continuous function on R such that f (1/(4n))=sin e^n/(e^(n^2))+n^2/(n^2+1) Then the value of f(0) is

Let f : (0, oo) rarr R be a continuous function such that 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)) , is equal to

Let T >0 be a fixed real number. Suppose f is continuous function such that for all x in R ,f(x+T)=f(x)dot If I=int_0^Tf(x)dx , then the value of int_3^(3+3T)f(2x)dx is 3/2I (b) 2I (c) 3I (d) 6I

Let f:R rarr R be a continuous function such that f(x)-2f(x/2)+f(x/4)=x^(2) . f'(0) is equal to

Let f:R rarr R be a continuous function such that f(x)-2f(x/2)+f(x/4)=x^(2) . f(3) is equal to

Let f : R rarr R be a differentiable function at x = 0 satisfying f(0) = 0 and f'(0) = 1, then the value of lim_(x to 0) (1)/(x) . sum_(n=1)^(oo)(-1)^(n).f((x)/(n)) , is a. 0 b. -log2 c. 1 d. e

Let f:[1,oo] be a differentiable function such that f(1)=2. If 6int_1^xf(t)dt=3xf(x)-x^3 for all xgeq1, then the value of f(2) is

Let f:R to R be a differentiable function such that f(x)=x^(2)+int_(0)^(x)e^(-t)f(x-t)dt . f(x) increases for

ARIHANT MATHS-DEFINITE INTEGRAL-Exercise (Questions Asked In Previous 13 Years Exam)
  1. Let f: R to R be a continuous function which satisfies f(x)= int0^xf(...

    Text Solution

    |

  2. The total number of distinct x in R for which |{:(x,x^(2),1+x^(3)...

    Text Solution

    |

  3. Let f(x)=7tan^8x+7tan^6x-3tan^4x-3tan^2x for all x in (-pi/2,pi/2) . ...

    Text Solution

    |

  4. Let f'(x)=(192x^(3))/(2+sin^(4)pix) for all x epsilonR with f(1/2)=0. ...

    Text Solution

    |

  5. The option(s) with the values of aa n dL that satisfy the following eq...

    Text Solution

    |

  6. Let F:RtoR be a thrice differntiable function. Suppose that F(1)=0,F(3...

    Text Solution

    |

  7. Let F:RtoR be a thrice differntiable function. Suppose that F(1)=0,F(3...

    Text Solution

    |

  8. If f(x)=x-[x], where [x] is the greatest integer less than or equal to...

    Text Solution

    |

  9. If alpha=int0^1(e^(9x+3tan^(-1)x))((12+9x^2)/(1+x^2))dx where tan^(-1)...

    Text Solution

    |

  10. The integral overset(pi//2)underset(pi//4)int (2 cosecx)^(17)dx is equ...

    Text Solution

    |

  11. Let f:[0,2]vecR be a function which is continuous on [0,2] and is diff...

    Text Solution

    |

  12. Match the conditions/ expressions in Column I with statement in Column...

    Text Solution

    |

  13. Find x+y+z

    Text Solution

    |

  14. The value of int0^1 4x^3{(d^2)/(dx^2)(1-x^2)^5}dx is

    Text Solution

    |

  15. The value of the integral int(-pi//2)^(pi//2) (x^(2) + log" (pi-x)/(pi...

    Text Solution

    |

  16. The value of int(In2)^(In3) (x sinx)dx is

    Text Solution

    |

  17. Let f:[1,oo] be a differentiable function such that f(1)=2. If 6int1...

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

  20. Let f:[0,1]toR (the set of all real numbers ) be a function. Suppose t...

    Text Solution

    |

  21. Which of the following is true?

    Text Solution

    |