Home
Class 12
MATHS
Let f(x) be a funntion satifying f'(x)=f...

Let f(x) be a funntion satifying f'(x)=f(x) with f(0)=1 and g(x) be the function satisfying `f(x)+g(x)=x^(2)`. The, value of integral ` int_(0)^(1)f(x)g(x)dx` is,

A

`(1)/(4)(e-7)`

B

`(1)/(4)(e-2)`

C

`(1)/(4)(e-3)`

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
D
Promotional Banner

Topper's Solved these Questions

  • DEFINITE INTEGRALS

    OBJECTIVE RD SHARMA|Exercise Chapter Test 1|60 Videos

  • CONTINUITY AND DIFFERENTIABILITY

    OBJECTIVE RD SHARMA|Exercise Exercise|86 Videos

  • DERIVATIVE AS A RATE MEASURER

    OBJECTIVE RD SHARMA|Exercise Exercise|26 Videos

Similar Questions

Explore conceptually related problems

Let f(x) be a function satisfying f\'(x)=f(x) with f(0)=1 and g(x) be the function satisfying f(x)+g(x)=x^2 . Then the value of integral int_0^1 f(x)g(x)dx is equal to (A) (e-2)/4 (B) (e-3)/2 (C) (e-4)/2 (D) none of these

Let f(x) be a function satisfying f'(x)=f(x) with f(0)=1 and g(x) be a function that satisfies f(x)+g(x)=x^(2). Then the value of the integral int_(0)^(1)f(x)g(x)dx, is

If a function f(x) satisfies f'(x)=g(x) . Then, the value of int_(a)^(b)f(x)g(x)dx is

Let f(x) and g(x) be two functions satisfying f(x^(2))+g(4-x)=4x^(3), g(4-x)+g(x)=0 , then the value of int_(-4)^(4)f(x^(2))dx is :

Let f(x) be a continuous function on [0,4] satisfying f(x)f(4-x)=1. The value of the definite integral int_(0)^(4)(1)/(1+f(x))dx equals -

If f(x) and g(x) are continuous functions satisfying f(x) = f(a-x) and g(x) + g(a-x) = 2 , then what is int_(0)^(a) f(x) g(x)dx equal to ?

OBJECTIVE RD SHARMA-DEFINITE INTEGRALS-Chapter Test 2
  1. The value of the integral int(0)^(2)x[x]dx

    Text Solution

    |

  2. The value of integral sum (k=1)^(n) int (0)^(1) f(k - 1+x) dx is

    Text Solution

    |

  3. Let f(x) be a funntion satifying f'(x)=f(x) with f(0)=1 and g(x) be th...

    Text Solution

    |

  4. If I=int(0)^(1) cos{ 2 "cot"^(-1)sqrt((1-x)/(1+x))}dx then

    Text Solution

    |

  5. The value of int(a)^(a+(pi//2))(sin^(4)x+cos^(4)x)dx is

    Text Solution

    |

  6. The vaue of int(-1)^(2) (|x|)/(x)dx is

    Text Solution

    |

  7. The value of int0^1 (x^(3))/(1+x^(8))dx is

    Text Solution

    |

  8. The value of int(0)^(3) xsqrt(1+x)dx, is

    Text Solution

    |

  9. The value of the integral int(0)^(1) log sin ((pix)/(2))dx is

    Text Solution

    |

  10. The value of the integral int(0)^(pi)x log sin x dx is

    Text Solution

    |

  11. If I(1)=int(0)^(oo) (dx)/(1+x^(4))dx and I(2)underset(0)overset(oo)in...

    Text Solution

    |

  12. If f(x)={{:(x,"for " x lt 1),(x-1,"for " x ge1):},"then" int(0)^(2) x...

    Text Solution

    |

  13. The value of the integral int(0)^(2) (1)/((x^(2)+1)^(3//2))dx is

    Text Solution

    |

  14. If int(0)^(2a) f(x)dx=int(0)^(2a) f(x)dx, then

    Text Solution

    |

  15. If int(0)^(36) (1)/(2x+9)dx =log k, is equal to

    Text Solution

    |

  16. The value of the integral int(0)^(pi//2) sin^(6) x dx, is

    Text Solution

    |

  17. If int(0)^(oo) e^(-x^(2))dx=sqrt((pi)/(2))"then"int(0)^(oo) e^(-ax^(2)...

    Text Solution

    |

  18. The value of the integral int 0^oo 1/(1+x^4)dx is

    Text Solution

    |

  19. If int(pi//2)^(x) sqrt(3-2sin^(2)u) dx+int(dx)^(dy) equal pi//2

    Text Solution

    |

  20. The value of alpha in [0,2pi] which does not satify the equation int(p...

    Text Solution

    |