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

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

B

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

C

`(e^(x))/(2-e)`

D

`(2e^(x))/(3-e)`

Text Solution

Verified by Experts

The correct Answer is:
B
Promotional Banner

Topper's Solved these Questions

  • INTEGRAL CALCULUS - 2

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

  • INTEGRAL CALCULUS - 2

    VMC MODULES ENGLISH|Exercise JEE Advanced (Archive)|103 Videos

  • INTEGRAL CALCULUS - 2

    VMC MODULES ENGLISH|Exercise JEE Advanced (Archive)|103 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

int_(0)^(a)f(x)dx

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

If int_0^af(2a-x)dx=m and int_0^af(x)dx=n, then int_0^(2a) f(x) dx is equal to

If f(a+x)=f(x), then int_(0)^(na) f(x)dx is equal to (n in N)

IF f(x+f(y))=f(x)+y AA x, y in R and f(0)=1 , then int_(0)^(10)f(10-x)dx is equal to

If f(0) = 1 , f(2) = 3, f'(2) = 5 and f'(0) is finite, then int_(0)^(1)x. f^''(2x) dx is equal to

If f(2a-x)=-f(x), prove that int_0^(2a)f(x)dx=0

Let a gt 0 and f(x) is monotonic increase such that f(0)=0 and f(a)=b, "then " int_(0)^(a) f(x) dx +int_(0)^(b) f^(-1) (x) dx is equal to

int e^x {f(x)-f'(x)}dx= phi(x) , then int e^x f(x) dx is

VMC MODULES ENGLISH-INTEGRAL CALCULUS - 2 -Level - 1
  1. The area of the smaller region in which the curve y=[(x^(3))/(100)+(x...

    Text Solution

    |

  2. Consider a rectangle ABCD formed by the points A=(0,0), B= (6, 0), C =...

    Text Solution

    |

  3. If f'(x) = f(x)+ int (0)^(1)f (x) dx and given f (0) =1, then int f (x...

    Text Solution

    |

  4. (sin 2 kx)/(sin x)=2[cos x + cos 3 x + …+cos (2k -1)x], then value of ...

    Text Solution

    |

  5. If int0^1(sint)/(1+t)dt=alpha, then the value of the integral int(4pi-...

    Text Solution

    |

  6. If n gt 1. Evaluate underset(0)overset(oo)int(dx)/((x+sqrt(1+x^(2)))^(...

    Text Solution

    |

  7. Let f(x) and g(x) be two functions satisfying f(x^(2))+g(4-x)=4x^(3),...

    Text Solution

    |

  8. f,g,h are continuous in [0,1],f(a-x)=f(x),g(a-x)=-g(x),3h(x)-4h(a-x)=5...

    Text Solution

    |

  9. The value of int(1)^(e)((tan^(-1))/x+(logx)/(1+x^(2)))dx is

    Text Solution

    |

  10. Area bounded by x-axis and the curve f(x) = e^[x].e^|x|.e^{x} between ...

    Text Solution

    |

  11. P(x) is a non-zero polynomial such that P(0)=0 and P(x^3)=x^4P(x),P'(1...

    Text Solution

    |

  12. Let lambda=int0^1(dx)/(1+x^3), p=lim(n rarr oo)[prod(r=1)^n(n^3+r^3)/(...

    Text Solution

    |

  13. Let f: (0, infty) rarr R and F (x) = int(0) ^(x) f(t) dt . If F(x^(2)...

    Text Solution

    |

  14. If f(x) is a function satisfying f(1/x)+x^2f(x)=0 for all nonzero x , ...

    Text Solution

    |

  15. The value of int1^2(x^([x^2])+[x^2]^x)dx, where [.] denotes the greate...

    Text Solution

    |

  16. if f(x) = |(cosx,e^(x^(2)),2x cos ^(2) x//2),(x^(2) ,sec x,sin x + x^(...

    Text Solution

    |

  17. Evaluate: int0^2(dx)/((17+8x-4x^2)[e^(6(1-x))+1)

    Text Solution

    |

  18. The value of x satisfying int(0)^(2[x+14]){(x)/(2)} dx=int(0)^({x})[x...

    Text Solution

    |

  19. If f(x) is a continous function such that f(x)|0,AA x in[2,10] and int...

    Text Solution

    |

  20. Let f be a one-one function such that f(x).f(y) + 2 = f(x) + f(y) + f(...

    Text Solution

    |