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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.
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