Home
Class 12
MATHS
If f'(x) = f(x)+ int (0)^(1)f (x) dx and...

If `f'(x) = f(x)+ int _(0)^(1)f (x)` dx and given `f (0) =1,` then `int f (x) dx` is equal to :

A

`(2)/(3-e) e ^(x) +((3-e)/(1-e))x+C`

B

`(2)/(3-e ) e ^(x) +((1-e)/(3-e))x +C`

C

`(3)/(2-e)e ^(x)+ ((1+e)/(3+e))x +C`

D

`(2)/(2-e) e ^(x) +((1-e)/(3+e))x +C`

Text Solution

Verified by Experts

The correct Answer is:
B
Promotional Banner

Topper's Solved these Questions

  • INDEFINITE AND DEFINITE INTEGRATION

    VK JAISWAL|Exercise EXERCISE (ONE OR MORE THAN ONE ANSWER IS/ARE CORRECT)|16 Videos

  • INDEFINITE AND DEFINITE INTEGRATION

    VK JAISWAL|Exercise EXERCISE (COMPREHENSION TYPE PROBLEMS)|17 Videos

  • HYPERBOLA

    VK JAISWAL|Exercise Exercise-4 : Subjective Type Problems|3 Videos

  • INVERSE TRIGONOMETRIC FUNTIONS

    VK JAISWAL|Exercise Exercise-5 : Subjective Type Problems|6 Videos

Similar Questions

Explore conceptually related problems

If f'(x)=f(x)+int_(0)^(1)f(x)dx ,given f(0)=1 , then the value of f(log_(e)2) is

If f(x) = f(a+x) and int_(0)^(a) f(x) dx = k, "then" int _(0)^(na) f(x) dx is equal to

if int_(0)^(1)f(x)dx=1 and f(2x)=2f(x) then 3int_(1)^(2)f(x)dx is equal to

if f(x)=|x-1| then int_(0)^(2)f(x)dx is

If int f(x)dx=F(x), then int x^(3)f(x^(2))dx is equal to:

If int f(x)dx=f(x), then int{f(x)}^(2)dx is equal to

If int_(-1)^(1)f(x)dx=0 then

VK JAISWAL-INDEFINITE AND DEFINITE INTEGRATION-EXERCISE (SUBJECTIVE TYPE PROBLEMS)
  1. If f'(x) = f(x)+ int (0)^(1)f (x) dx and given f (0) =1, then int f (x...

    Text Solution

    |

  2. int (x+ ( cos^(-1)3x )^(2))/(sqrt(1-9x ^(2)))dx = (1)/(k (1)) ( sqrt(1...

    Text Solution

    |

  3. If int (0)^(oo) (x ^(3))/((a ^(2)+ x ^(2)))dx = (1)/(ka ^(6)), then fi...

    Text Solution

    |

  4. int( (x^2+1)dx)/x

    Text Solution

    |

  5. If int (x ^(6) +x ^(4)+x^(2)) sqrt(2x ^(4) +3x ^(2)+6) dx = ((ax ^(6) ...

    Text Solution

    |

  6. int( x^2+3)/(x^2+2)dx

    Text Solution

    |

  7. The value of int (tan x )/(tan ^(2) x + tan x+1)dx =x -(2)/(sqrtA) tan...

    Text Solution

    |

  8. Let int (0)^(1) (4x ^(3) (1+(x ^(4)) ^(2010)))/((1+x^(4))^(2012))dx = ...

    Text Solution

    |

  9. Let int ( 1) ^(sqrt5)(x ^(2x ^(2)+1) +ln "("x ^(2x ^(2x ^(2+1)))")")dx...

    Text Solution

    |

  10. If int (dx )/(cos ^(3) x-sin ^(3))=A tan ^(-1) (f (x)) +bln |(sqrt2+f ...

    Text Solution

    |

  11. Find the value of |a| for which the area of triangle included between ...

    Text Solution

    |

  12. Let I = int (0) ^(pi) x ^(6) (pi-x) ^(8)dx, then (pi ^(15))/((""^(15) ...

    Text Solution

    |

  13. int( x^3)/(x^2-3)dx

    Text Solution

    |

  14. If a continuous function f on [0,a] satisfies f(x)f(a-x)=1,agt0, then ...

    Text Solution

    |

  15. If {x} denotes the fractional part of x, then I = int (0) ^(100) (sqrt...

    Text Solution

    |

  16. int( x^3)/(x^2-2)dx

    Text Solution

    |

  17. IF M be the maximum valur of 72 int (0) ^(y) sqrt(x ^(4) +(y-y^(2))^(2...

    Text Solution

    |

  18. Find the number points where f (theta) = int (-1)^(1) (sin theta dx )/...

    Text Solution

    |

  19. underset(nrarroo)lim[(1)/(sqrtn)+(1)/(sqrt(2n))+(1)/(sqrt(3n))+...+(1)...

    Text Solution

    |

  20. The maximum value of int (-pi//2) ^(2pi//2) sin x. f (x) dx, subject t...

    Text Solution

    |

  21. Given a funtion g, continous everywhere such that g (1)=5 and int (0)^...

    Text Solution

    |