Home
Class 12
MATHS
Find the area of the region included bet...

Find the area of the region included between `y^(2)=9x" and "y=x`.

Text Solution

Verified by Experts

The correct Answer is:
N/a
We have, `y^(2)=9x`
`rArrx^(2)=9x`
`rArrx^(2)-9x=0`
`rArrx(x-9)=0`
`rArrx=0, 9`

`:. " Area opf shaded region,"A=int_(0)^(9)(sqrt(9x)-x)dx=int_(0)^(9)3x^(1//2)dx-int_(0)^(9)x dx`
`=[3. (x^(3//2))/3 .2]_(0)^(9)-[(x^(2))/2]_(0)^(9)`
`=[(3.3^(2/3xx2))/3 .2-0][81/2-0]`
`=54-81/2=(108-81)/2=27/2" sq units"`
Promotional Banner

Topper's Solved these Questions

  • APPLICATION OF INTEGRALS

    NCERT EXEMPLAR ENGLISH|Exercise Long Answer Type Questions|16 Videos

  • APPLICATION OF INTEGRALS

    NCERT EXEMPLAR ENGLISH|Exercise Objective Type Questions|22 Videos

  • APPLICATION OF DERIVATIVES

    NCERT EXEMPLAR ENGLISH|Exercise Fillers|5 Videos

  • CONTINUITY AND DIFFERENTIABILITY

    NCERT EXEMPLAR ENGLISH|Exercise True/False|10 Videos

Similar Questions

Explore conceptually related problems

Find the area of the region bounded by the curve y^(2)=9x" and " y=3x .

Find the area of the region included between the parabola y^2=x and the line x+y=2 .

Find the area of the region included between the parabola y^2=x and the line x+y=2 .

Find the area of the region bounded by the curve y^(2)=2x" and "x^(2)+y^(2)=4x .

Find the area of the region bounded by the curve y^(2)=4x" and " x^(2)=4y .

Find the area of the region bounded by the curve y^(2)=4x" and " x^(2)=4y .

Find the area of the region enclosed by the curves y=x^(2) and y = 2x

Find the area of the region bounded by the curves y^(2)=x+1 and y^(2)= -x +1 .

Find the area of the region enclosed by y=-5x-x^(2) and y=x on interval [-1,5]

Find the area of the region enclosed by the curves y=xlogx and y=2x-2x^2dot

NCERT EXEMPLAR ENGLISH-APPLICATION OF INTEGRALS-Objective Type Questions
  1. Find the area of the region included between y^(2)=9x" and "y=x.

    Text Solution

    |

  2. The area of the region bounded by the Y-"axis" y = "cos" x and y = "si...

    Text Solution

    |

  3. The area of the region bounded by the curve x^(2)=4y and the straight ...

    Text Solution

    |

  4. The area of the region bounded by the curve y=sqrt(16-x^(2)) and X-axi...

    Text Solution

    |

  5. Find the area of the region in the first quadrant enclosed by the y-ax...

    Text Solution

    |

  6. Area of the regionbounded by the curve y = "cos" x between x = 0 and x...

    Text Solution

    |

  7. The area of the region bounded by parabola y^(2)=x and the straight li...

    Text Solution

    |

  8. The area of the region bounded by the curve y = "sin" x between the or...

    Text Solution

    |

  9. The area of the region bounded by the ellipse (x^(2))/25+y^(2)/16=1 is

    Text Solution

    |

  10. The area of the region by the circle x^(2)+y^(2)=1 is

    Text Solution

    |

  11. The area of the region bounded by the curve y = x + 1 and the lines x=...

    Text Solution

    |

  12. The area of the region bounded by the curve x=2y+3 and the lines y=1, ...

    Text Solution

    |

  13. The area of the region bounded by the Y-"axis" y = "cos" x and y = "si...

    Text Solution

    |

  14. Using integration, find the area bounded by the curve x^2=4y and the l...

    Text Solution

    |

  15. The area of the region bounded by the curve y=sqrt(16-x^(2)) and X-axi...

    Text Solution

    |

  16. Area of the region in the first quadrant exclosed by the X-axis, the l...

    Text Solution

    |

  17. Area of the regionbounded by the curve y = "cos" x between x = 0 and x...

    Text Solution

    |

  18. The area of the region bounded by parabola y^(2)=x and the straight li...

    Text Solution

    |

  19. The area of the region bounded by the curve y = "sin" x between the or...

    Text Solution

    |

  20. The area of the region bounded by the ellipse (x^(2))/25+y^(2)/16=1 is

    Text Solution

    |

  21. The area of the region by the circle x^(2)+y^(2)=1 is

    Text Solution

    |