Home
Class 12
MATHS
The area bounded by the curves y = |x| -...

The area bounded by the curves y = |x| - 1 and `y = -|x| +1` is equal to

A

1

B

2

C

`sqrt2`

D

4

Text Solution

Verified by Experts

The correct Answer is:
B
Let A be the required area. Then,
A=Area enclosed by seuared ABCD
`implies A=2` sq. unit.
LLITER `A=4("Area of" Delta` CAB)
`impliesA=4underset(0)overset(1)(int)y dx`
`impliesA=4 underset(0)overset(1)(int)(-x+1)dx`
`impliesA=4[(-x^(2))/(2)+x]_(0)^(1)=2` sq. unit
Promotional Banner

Topper's Solved these Questions

  • AREAS OF BOUNDED REGIONS

    OBJECTIVE RD SHARMA ENGLISH|Exercise Exercise|61 Videos

  • AREAS OF BOUNDED REGIONS

    OBJECTIVE RD SHARMA ENGLISH|Exercise Chapter Test|60 Videos

  • ALGEBRAIC INEQUATIONS

    OBJECTIVE RD SHARMA ENGLISH|Exercise Exercise|39 Videos

  • CARTESIAN PRODUCT OF SETS AND RELATIONS

    OBJECTIVE RD SHARMA ENGLISH|Exercise Chapter Test|30 Videos

Similar Questions

Explore conceptually related problems

Area bounded by the curves y=x^2 - 1 and x+y=3 is:

Using integration, find the area bounded by the curves y = |x-1| and y = 3-|x| .

Using integration, find the area bounded by the curves y = |x-1| and y = 3-|x| .

The area of the region bounded by the curve y = x^(2) and y = x is equal to

The area bounded between curves y^2 = x and y= |x|

The area bounded by the curve y=3/|x| and y+|2-x|=2 is

Area bounded by the curves y=|x-1|, y=0 and |x|=2

The area bounded by the curves y=x,y=x^(3) is

The area bounded by the curve y = cos^-1(cos x) and y=|x-pi| is

Find the area bounded by curve y = x^(2) - 1 and y = 1 .

OBJECTIVE RD SHARMA ENGLISH-AREAS OF BOUNDED REGIONS-Chapter Test
  1. The area bounded by the curves y = |x| - 1 and y = -|x| +1 is equal to

    Text Solution

    |

  2. Area bounded by the curves y=|x-1|, y=0 and |x|=2

    Text Solution

    |

  3. The area inside the parabola 5x^2-y=0 but outside the parabola 2x^2-y+...

    Text Solution

    |

  4. The area enclosed between the curve y^(2)(2a-x)=x^(3) and the line x=2...

    Text Solution

    |

  5. Area bounded by the curve x y^2=a^2(a-x) and the y-axis is (pia^2)/2s ...

    Text Solution

    |

  6. The area of the loop of the curve ay^(2)=x^(2)(a-x) is

    Text Solution

    |

  7. find the area common to the circle x^2y^2=16 a^2 and the parabola y^2=...

    Text Solution

    |

  8. The line y=m x bisects the area enclosed by the curve y=1+4x-x^2 and t...

    Text Solution

    |

  9. The area between the curve y=xsin x and x-axis where o le x le 2 pi ,...

    Text Solution

    |

  10. The area bounded by the curves y=e^(x),y=e^(-x) and y=2, is

    Text Solution

    |

  11. The area enclosed by the curves x=a sin^(3)t and y= a cos^(2)t is equa...

    Text Solution

    |

  12. If A(1) is the area enclosed by the curve xy=1, x-axis and the ordinat...

    Text Solution

    |

  13. If area bounded by the curve y^(2)=4ax and y=mx is a^(2)//3 , then the...

    Text Solution

    |

  14. The value of a for which the area between the curves y^(2) = 4ax and x...

    Text Solution

    |

  15. If the area bounded by the curve y=f(x), x-axis and the ordinates x=1 ...

    Text Solution

    |

  16. The area bounded by the curve y = sin2x, axis and y=1, is

    Text Solution

    |

  17. The area between the curve x=-2y^(2)and x=1-3y^(2), is

    Text Solution

    |

  18. The area between the curves y=cosx, x-axis and the line y=x+1, is

    Text Solution

    |

  19. If the area bounded by the curve y=x^2+1 and the tangents to it drawn ...

    Text Solution

    |

  20. The positive value of the parmeter 'a' for which the area of the figur...

    Text Solution

    |

  21. The area in square units bounded by the curves y=x^(3),y=x^(2) and the...

    Text Solution

    |