Question

The area bounded by the curve y = x|x|, x-axis and the ordinates x = −1 and x = 1 is given by ______.

Options

• 0

• `1/3`

• `2/3`

• `4/3`

Answer 1

The area bounded by the curve y = x|x|, x-axis and the ordinates x = −1 and x = 1 is given by `underlinebb(2/3)`.

Explanation:

Area bounded by the curve and x-axis is `int_-1^1|y|dx`

Since y = x|x|, |y| = x²

Therefore,

Area = `int_-1^1 x^2dx`

= `2 int_0^1x^2dx`

= `2[x^3/3]_0^1`

∴ Area = `2/3`