Home
Class 12
MATHS
y=f(x) is a function which satisfies f(0...

`y=f(x)` is a function which satisfies `f(0)=0, f"''(x)=f'(x)` and `f'(0)=1` then the area bounded by the graph of `y=f(x)`, the lines `x=0, x-1=0` and `y+1=0` is

A

e

B

e-2

C

e-1

D

e+1

Text Solution

Verified by Experts

The correct Answer is:
C
Promotional Banner

Topper's Solved these Questions

  • AREA OF BOUNDED REGIONS

    ARIHANT MATHS ENGLISH|Exercise Exercise (More Than One Correct Option Type Questions)|5 Videos

  • AREA OF BOUNDED REGIONS

    ARIHANT MATHS ENGLISH|Exercise Exercise (Statement I And Ii Type Questions)|5 Videos

  • AREA OF BOUNDED REGIONS

    ARIHANT MATHS ENGLISH|Exercise Exercise For Session 2|19 Videos

  • BIONOMIAL THEOREM

    ARIHANT MATHS ENGLISH|Exercise Exercise (Questions Asked In Previous 13 Years Exam)|21 Videos

Similar Questions

Explore conceptually related problems

A function f : R -> R^+ satisfies f(x+y)= f(x) f(y) AA x in R If f'(0)=2 then f'(x)=

If y=f(x) is the solution of equation ydx+dy=-e^(x)y^(2) dy, f(0)=1 and area bounded by the curve y=f(x), y=e^(x) and x=1 is A, then

Let f(x) be a real valued function satisfying the relation f(x/y) = f(x) - f(y) and lim_(x rarr 0) f(1+x)/x = 3. The area bounded by the curve y = f(x), y-axis and the line y = 3 is equal to

Let f(x)=x^(3)+x^(2)+x+1, then the area (in sq. units) bounded by y=f(x), x=0, y=0 and x=1 is equal to

If a function satisfies the relation f(x) f''(x)-f(x)f'(x)=(f'(x))^(2) AA x in R and f(0)=f'(0)=1, then The value of lim_(x to -oo) f(x) is

Let f:R->R be a function such that f((x+y)/3)=(f(x)+f(y))/3 ,f(0) = 0 and f'(0)=3 ,then

Let f:R->R be a function such that f((x+y)/3)=(f(x)+f(y))/3 ,f(0) = 0 and f'(0)=3 ,then

If y=(f_(0)f_(0)f)(x)andf(0)=0,f'(0)=2 then y'(0) is equal to

If the function / satisfies the relation f(x+y)+f(x-y)=2f(x),f(y)AAx , y in R and f(0)!=0 , then

If f(x) is a differentiable function satisfying |f'(x)|le4AA x in [0, 4] and f(0)=0 , then

ARIHANT MATHS ENGLISH-AREA OF BOUNDED REGIONS-Exercise (Single Option Correct Type Questions)
  1. If the area bounded by the corve y=x^(2)+1, y=x and the pair of lines ...

    Text Solution

    |

  2. Suppose y=f(x) and y=g(x) are two functions whose graphs intersect at ...

    Text Solution

    |

  3. Let 'a' be a positive constant number. Consider two curves C1: y=e^x...

    Text Solution

    |

  4. 3 point O(0,0),P(a,a^2),Q(-b,b^2)(agt0,bgt0) are on the parabola y=x^2...

    Text Solution

    |

  5. Area enclosed by the graph of the function y= In^2x-1 lying in the 4...

    Text Solution

    |

  6. The area bounded by y = 2-|2-x| and y=3/|x| is:

    Text Solution

    |

  7. Suppose g(x)=2x+1 and h(x)=4x^(2)+4x+5 and h(x)=(fog)(x). The area enc...

    Text Solution

    |

  8. The area bounded by the curves y=-sqrt(-x) and x=-sqrt(-y) where x,yle...

    Text Solution

    |

  9. y=f(x) is a function which satisfies f(0)=0, f"''(x)=f'(x) and f'(0)=1...

    Text Solution

    |

  10. The area of the region enclosed between the curves x=y^(2)-1 and x=|x|...

    Text Solution

    |

  11. The area bounded by the curve y=xe^(-x),y=0 and x=c, where c is the x-...

    Text Solution

    |

  12. If (a,0), agt 0, is the point where the curve y=sin 2x-sqrt3 sin x cut...

    Text Solution

    |

  13. The curve y=ax^2+bx +c passes through the point (1,2) and its tangent ...

    Text Solution

    |

  14. A function y=f(x) satisfies the differential equation (dy)/(dx)-y= co...

    Text Solution

    |

  15. The ratio between masses of two planets is 3 : 5 and the ratio between...

    Text Solution

    |

  16. Area bounded by y=f^(-1)(x) and tangent and normal drawn to it at poin...

    Text Solution

    |

  17. If f(x)=x-1 and g(x)=|f|(x)|-2|, then the area bounded by y=g(x) and t...

    Text Solution

    |

  18. Let S = {(x,y): (y(3x-1))/(x(3x-2))<0}, S'= {(x,y) in AxxB: -1 leqAleq...

    Text Solution

    |

  19. The area of the region bounded between the curves y=e||x|In|x||,x^2+y...

    Text Solution

    |

  20. A point P lying inside the curve y = sqrt(2ax-x^2) is moving such that...

    Text Solution

    |