Question

The area bounded by the curve `y" "=" "x" "|" "x" "|` , x-axis and the ordinates `x" "=" "" "1` and `x" "=" "1` is given by (A) 0 (B) `1/3` (C) `2/3` (D) `4/3` [Hint : `y=x^2` if `x" ">" "0` and `y=-x^2` if `x" "<" "0` ].

Answer 1

Correct Answer - C
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.