Home
Class 12
MATHS
The area bounded by the curve a^(2)y=x^(...

The area bounded by the curve `a^(2)y=x^(2)(x+a)` and the x-axis is

A

`a^(2)//3` sq. units

B

`a^(2)//4` sq. units

C

`3a^(2)//4` sq. units

D

`a^(2)//12` sq. units

Text Solution

Verified by Experts

The correct Answer is:
D
The curve is `y=(x^(2)(x+a))/(a^(2))`, which is a cubic polynomial.
Since `(x^(2)(x+a))/(a^(2))=0` has a repeated root x=0, it touchses x-axis at (0,0) and intersects at (-a,0).

`"Required area "=int_(-a)^(0)ydx `
`=int_(-a)^(0)[(x^(2)(x+a))/(a^(2))]dx`
`=a^(2)//12` sq. units.
Promotional Banner

Topper's Solved these Questions

  • AREA

    CENGAGE|Exercise Exercise (Multiple)|10 Videos

  • AREA

    CENGAGE|Exercise Exercise (Comprehension)|21 Videos

  • AREA

    CENGAGE|Exercise Exercise 9.3|7 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 bounded by the curve a^2y=x^2(x+a) and the x-axis is (a^2)/3s qdotu n i t s (b) (a^2)/4s qdotu n i t s (3a^2)/4s qdotu n i t s (d) (a^2)/(12)s qdotu n i t s

The area bounded by the curve y=x^(2)(x-1)^(2) with the x - axis is k sq. units. Then the value of 60 k is equal to

What is the area bounded by the curve y = 4x-x^(2) -3 and the x-axis ?

The area bounded by the curves y^(2)=x^(3) and |y|=2x

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

Area of the region bounded by the curve y=x^(2)-5x+4 and the X-axis is

The area bounded by the curve y=sin^(2)x-2 sin x and the x-axis, where x in [0, 2pi] , is

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

Area bounded by the curve y=x^(2)+x-6 and the X-axis is

CENGAGE-AREA-Exercise (Single)
  1. Let f(x) = minimum (x+1, sqrt(1-x))" for all "x le 1. Then the area bo...

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

  4. The area between the curve y=2x^(4)-x^(2), the x-axis, and the ordinat...

    Text Solution

    |

  5. The area of the closed figure bounded by x=-1x=2, and y={{:(-x^(2)+2",...

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

  8. The area bounded by the curve y=x(1-log(e)x) and x-axis is

    Text Solution

    |

  9. The area inside the parabola 5x^(2)-y=0 but outside the parabola 2x^(2...

    Text Solution

    |

  10. Area enclosed between the curves |y|=1-x^2a n dx^2+y^2=1 is (3pi-8)/3 ...

    Text Solution

    |

  11. If A(n) is the area bounded by y=x and y=x^(n), n in N, then A(2).A(3)...

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

  16. The area bounded by the curve y^(2)=1-x and the lines y=([x])/(x),x=-...

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

  19. Find the area enclosed between the curves: y = loge (x + e) , x = loge...

    Text Solution

    |

  20. Find the area enclosed the curve y=sin x and the X-axis between x=0 an...

    Text Solution

    |