The area bounded by the curve `y = x | x |` , x-axis and the ordinates `x = 1` is given by
[Hint : `y=x^2` if `x" ">" "0` and `y=-x^2` if `x" "<" "0` ].

Options

A. 0
B. `(1)/(3)`
C. `(2)/(3)`
D. `(4)/(3)`

Answer

C

Explanation

Given, `y=x|x|={(" "x^(2)","x ge0),(-x^(2)","x lt0):}`

` :. ` Required area `=2 int_(0)^(1)x|x|=2 int_(0)^(1)x^(2)dx`
`=2[(x^(3))/(3)](0)^(1)=(2)/(3)(1^(3)-0^(3))`
`=(2)/(3)` sq. unit.