Home
Class 12
MATHS
The area of the region bonded by y=e^(x)...

The area of the region bonded by `y=e^(x),y=e^(-x),x=0` and x = 1 is

A

`e+(1)/(e)`

B

`log(4//e)`

C

`4log(4//e)`

D

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

Text Solution

Verified by Experts

The correct Answer is:
D
The graph of the functions is as shown in the following figure :

`A=int_(0)^(1)(e^(x)-e^(-x))dx`
`=(e^(x)+e^(-x))_(0)^(1)`
`=(e+e^(-1))-(1+1)`
`=e+(1)/(e)-2`
Promotional Banner

Topper's Solved these Questions

  • AREA

    CENGAGE|Exercise Comprehension Type|2 Videos

  • AREA

    CENGAGE|Exercise Multiple Correct Answer Type|3 Videos

  • APPLICATIONS OF DERIVATIVES

    CENGAGE|Exercise Question Bank|29 Videos

  • AREA UNDER CURVES

    CENGAGE|Exercise Question Bank|20 Videos

Similar Questions

Explore conceptually related problems

The area of the region bounded by y=x^(2)+2,y=-x,x=0 and x=1 is

The area of the region bounded by the curves y=e^(x), y=e^(-x) and x - axis in square units is equal to

The area of the figure bounded by y=e^(x-1),y=0,x=0 and x=2 is

If S be the area of the region enclosed by y=e^(-x^(2)), y=0, x=0 and x = 1. Then :

The area of the region bounded by the curves y=xe^(x),y=e^(x) and the lines x=+-1, is equal to

Which of the following is not the area of the region bounded by y= e^(x) and x=0 and y= e?

Find the area of the region bounded by y=x^2+1, y=x, x=0 and y=2 .

The area of the region bounded by y=1+|x+1|,x=-3,x=3,y=0 is

CENGAGE-AREA-Single Correct Answer Type
  1. The area enclosed between the curve y=sin^(2)x and y=cos^(2)x in the i...

    Text Solution

    |

  2. The area of the region enclosed by y=x^2 and y=sqrt(|x|) is

    Text Solution

    |

  3. The area of the region bonded by y=e^(x),y=e^(-x),x=0 and x = 1 is

    Text Solution

    |

  4. The area bounded by the curve y=|cos^(-1)(sinx)|-|sin^(-1)(cosx)| and ...

    Text Solution

    |

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

    Text Solution

    |

  6. The area in the first quadrant between x^2+y^2=pi^2 and y=sinx is

    Text Solution

    |

  7. The area bounded by the curves y=cos^(-1)x,y =sin^(-1) x and y=-pix^(3...

    Text Solution

    |

  8. The area bounded by the curve y=sin^(2)x-2 sin x and the x-axis, wher...

    Text Solution

    |

  9. Consider the functions f(x) and g(x), both defined from R rarrR and ar...

    Text Solution

    |

  10. Let function f(x) is defined in [-2,2] as f(x)={{:({x}",",-2lexle-1),(...

    Text Solution

    |

  11. The area bounded by y=x^(2)+2 and y=2|x|-cospi x is equal to

    Text Solution

    |

  12. Area bounded by f(x)=(x^(2)-1)/(x^(2)+1) and the line y = 1 is

    Text Solution

    |

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

    Text Solution

    |

  14. Area of region bounded by the curve y=(16-x^(2))/(4) and y=sec^(-1)[-s...

    Text Solution

    |

  15. Suppose y=f(x) and y=g(x) are two continuous functiond whose graphs in...

    Text Solution

    |

  16. The ratio of the areas of two regions of the curve C(1)-=4x^(2)+pi^(2)...

    Text Solution

    |

  17. The area bounded by the curves xsqrt3+y=2log(e)(x-ysqrt3)-2log(e)2, ...

    Text Solution

    |

  18. Area of region bounded by the curve y=(4-x^(2))/(4+x^(2)), 25y^(2)=9x ...

    Text Solution

    |

  19. Area bounded by the min. {|x|,|y|}=1 and the max. {|x|,|y|}=2 is

    Text Solution

    |

  20. Consider f(x)={{:(cosx,0lexlt(pi)/(2)),(((pi)/(2)-x)^(2),(pi)/(2)lexlt...

    Text Solution

    |