Home
Class 12
MATHS
Let f:RtoR be a differentiable function ...

Let `f:RtoR` be a differentiable function such that `f(x)=x^(2)+int_(0)^(x)e^(-t)f(x-t)dt`.
The value of `int_(0)^(1)f(x)dx` is

Promotional Banner

Topper's Solved these Questions

  • INVERSE TRIGONOMETRIC FUNCTIONS

    RESONANCE DPP ENGLISH|Exercise All Questions|15 Videos
  • MATRICES

    RESONANCE DPP ENGLISH|Exercise All Questions|7 Videos

Similar Questions

Explore conceptually related problems

Let f:RtoR be a differentiable function such that f(x)=x^(2)+int_(0)^(x)e^(-t)f(x-t)dt . y=f(x) 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

Let f:RtoR be a differntiable function satisfying f(x)=x^(2)+3int_(0)^(x)e^(-t^(3)).f(x-t^(3))dt . Then find f(x) .

Let f(x) be a differentiable function such that f(x)=x^2 +int_0^x e^-t f(x-t) dt then int_0^1 f(x) dx=

if f(x) is a differential function such that f(x)=int_(0)^(x)(1+2xf(t))dt&f(1)=e , then Q. int_(0)^(1)f(x)dx=

Let f(x) be a differentiable function satisfying f(x)=int_(0)^(x)e^((2tx-t^(2)))cos(x-t)dt , then find the value of f''(0) .

If f:RrarrR,f(x) is a differentiable function such that (f(x))^(2)=e^(2)+int_(0)^(x)(f(t)^(2)+(f'(t))^(2))dtAAx inR . The values f(1) can take is/are

Let f be a differentiable function such that f'(x) = f(x) + int_(0)^(2) f(x) dx and f(0) = (4-e^(2))/(3) . Find f(x) .

If f' is a differentiable function satisfying f(x)=int_(0)^(x)sqrt(1-f^(2)(t))dt+1/2 then the value of f(pi) is equal to

Let f(x) be a continuous and differentiable function such that f(x)=int_0^xsin(t^2-t+x)dt Then prove that f^('')(x)+f(x)=cosx^2+2xsinx^2

RESONANCE DPP ENGLISH-JEE MAINS-All Questions
  1. f:RrarrR be twice differentiable function satisfying f^(")(x)-5f^(')...

    Text Solution

    |

  2. Make the following expressions free from modulus sign : (x in R) (...

    Text Solution

    |

  3. Let f:RtoR be a differentiable function such that f(x)=x^(2)+int(0)^(x...

    Text Solution

    |

  4. let |{:(1+x,x,x^(2)),(x,1+x,x^(2)),(x^(2),x,1+x):}|=(1)/(6)(x-alpha(1)...

    Text Solution

    |

  5. The sum of first p -terms of a sequence is p(p+1)(p+2)dot the 10th ter...

    Text Solution

    |

  6. Lines whose equation are (x-3)/(2)=(y-2)/(3)=(z-1)/(lamda) and (x-2)/(...

    Text Solution

    |

  7. The solution set of the inequation 3^(72)(1/3)^x(1/3)^(sqrt(x))>1 is [...

    Text Solution

    |

  8. If the curves C1 : y= (In x)/x and C2 : y=lambdax^2 (where lambda is c...

    Text Solution

    |

  9. A die is rolled and showing any number is directly proportional to tha...

    Text Solution

    |

  10. If A=[{:(1,-1,1),(0,2,-3),(2,1,0):}] and B=(adjA) and C=5A, then find ...

    Text Solution

    |

  11. If the roots of the equation (x^2-b x)/(a x-c)=(m-1)/(m+1) are equal ...

    Text Solution

    |

  12. Find the value of a for which the sum of the squares of the roots of t...

    Text Solution

    |

  13. Lines whose equation are (x-3)/(2)=(y-2)/(3)=(z-1)/(lamda) and (x-2)/(...

    Text Solution

    |

  14. Let f(x)a n dg(x) be differentiable functions such that f^(prime)(x)g(...

    Text Solution

    |

  15. Let f(x)= 4x^(2) - 4ax + a^(2) - 2a + 2 such that minimum value fo the...

    Text Solution

    |

  16. Suppose that E1 and E2 are two events of a random experiment such that...

    Text Solution

    |

  17. If 1/3(log)3M+3(log)3N=1+(log)(0. 008)5, then

    Text Solution

    |

  18. Consider a quadratic equation az^(2)bz+c=0, where a,b and c are comple...

    Text Solution

    |

  19. Find tha value of the expression 2/log4(2000)^6+3/log5(2000)^6

    Text Solution

    |

  20. Find the whole area included between the curve x^2y^(2) = a^(2)(y^(2) ...

    Text Solution

    |