Home
Class 12
MATHS
Let f(x)=min (x+1,sqrt(1-x)) for all xlt...

Let `f(x)=min (x+1,sqrt(1-x))` for all `xlt=1.` Then the area bounded by `y=f(x)` and the x-axis is (a) `7/3` sq units (b) `1/6` sq units (c) `(11)/6` sq units (d) `7/6` sq units

A

`(7)/(3)` sq. units

B

`(1)/(6)` sq. units

C

`(11)/(6)` sq. units

D

`(7)/(6)` sq. units

Text Solution

Verified by Experts

The correct Answer is:
D

Required area =Shaded region
`=overset(1)underset(0)int(x_(2)-x_(1))dy` (integrating along y-axis)
`=overset(1)underset(0)int[(1-y^(2))-(y-1)]dy`
`=(7)/(6)` sq. unit
Promotional Banner

Topper's Solved these Questions

  • AREA

    CENGAGE PUBLICATION|Exercise Multiple Correct Answers Type|13 Videos

  • AREA

    CENGAGE PUBLICATION|Exercise Linkded Comprehension Type|21 Videos

  • AREA

    CENGAGE PUBLICATION|Exercise Concept Application Exercise 9.3|7 Videos

  • APPLICATIONS OF DERIVATIVES

    CENGAGE PUBLICATION|Exercise Subjective Type|2 Videos

  • BINOMIAL THEOREM

    CENGAGE PUBLICATION|Exercise Comprehension|11 Videos

Similar Questions

Explore conceptually related problems

The area bounded by the curves y=log_e x and y=(log_e x)^2 is (A) e-2 sq. units (B) 3-e sq. units (C) e sq. units (D) e-1 sq. units

The area enclosed by 2|x|+3|y|lt=6 is (a) 3 sq. units (b) 4 sq. units 12 sq. units (d) 24 sq. units

If f(x)=sinx ,AAx in [0,pi/2],f(x)+f(pi-x)=2,AAx in (pi/2,pi]a n df(x)=f(2pi-x),AAx in (pi,2pi], then the area enclosed by y=f(x) and the x-axis is (a) pi sq dot units (b) 2pi sq dot units (c) 2 sq dot units (d) 4 sq dot units

The area bounded by y = 3-|3-x| and y=6/(|x+1|) is

The area bounded by the curves y=|x|-1a n dy=-|x|+1 is 1 sq. units (b) 2 sq. units 2sqrt(2) sq. units (d) 4 sq. units

The area bounded by the parabolas y=(x+1)^2 and y=(x-1)^2a n dy=(x-1)^2 and the line y=1/4 is (a)4 sq. units (b) 1/6 sq. units 4/3 sq. units (d) 1/3 sq. units

The area bounded by the curves y=sqrt(x),2y+3=x , and x-axis in the 1st quadrant is (A) 18 sq. units (B) (27)/4 sq.units (C) 4/3 sq.units (D) 9 sq. units

The area bounded by the curves y=x(x-3)^2a n dy=x is________ (in sq. units)

The area (in square unit) bounded by the curve f(x)=4-|x| and the x-axis is -

A variable line x/a + y/b = 1 moves in such a way that the harmonic mean of a and b is 8. Then the least area of triangle made by the line with the coordinate axes is (1) 8 sq. unit (2) 16 sq. unit (3) 32 sq. unit (4) 64 sq. unit

CENGAGE PUBLICATION-AREA-Exercises - Single Correct Answer Type
  1. Area enclosed by the curve y=f(x) defined parametrically as x=(1-t^2)...

    Text Solution

    |

  2. Let f(x)=min (x+1,sqrt(1-x)) for all xlt=1. Then the area bounded by y...

    Text Solution

    |

  3. The area of the closed figure bounded by x=-1,y=0,y=x^2+x+1, and the t...

    Text Solution

    |

  4. The area bounded by the curve a^2y=x^2(x+a) and the x-axis is (a^2)/3s...

    Text Solution

    |

  5. The area between the curve y=2x^4-x^2, the axis, and the ordinates of ...

    Text Solution

    |

  6. The area of the closed figure bounded by x=-1,x=2,a n d y={-x^2+2,xlt...

    Text Solution

    |

  7. The value of the parameter a such that the area bounded by y=a^(2)x^(2...

    Text Solution

    |

  8. The positive valu of the parameter 'k' for which the area of the figu...

    Text Solution

    |

  9. The area bounded by the curve y=x(1-log(e)x) and x-axis is (a) (e^(2...

    Text Solution

    |

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

    Text Solution

    |

  11. Area enclosed between the curves |y|=1-x^2 and x^2+y^2=1 is (a) (3pi-8...

    Text Solution

    |

  12. If An is the area bounded by y=x and y=x^n ,n in \mathbb{N} ,then A2 A...

    Text Solution

    |

  13. The area of the region is 1st quadrant bounded by the y-axis, y=(x)/(4...

    Text Solution

    |

  14. The area of the closed figure bounded by y=(x^2)/2-2x+2 and the tangen...

    Text Solution

    |

  15. The area of the region bounded by x^(2)+y^(2)-2x-3=0 and y=|x|+1 is

    Text Solution

    |

  16. The area enclosed by the curve y=sqrt(4-x^2),ygeqsqrt(2)sin((xpi)/(2sq...

    Text Solution

    |

  17. The area bounded by the curve y^(2)(2-x)=x^(3) and x=2 is

    Text Solution

    |

  18. The area bounded by the curves y=(log)e xa n dy=((log)e x)^2 is

    Text Solution

    |

  19. The area bounded by y = 3-|3-x| and y=6/(|x+1|) is

    Text Solution

    |

  20. The area enclosed between the curves y=(log)e(x+e),x=(log)e(1/y), and ...

    Text Solution

    |