Question

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

[Hint: y = x² if x > 0 and y = –x² if x < 0]

विकल्प

• 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 `underline(2/3)`. 

Explanation:

When x > 0, |x| = x

∴ Equation of the curve  y = x²

When x < 0, |x| = -x

Equation of the curve y = -x²

Curve y = x |x|, x ≥ -1, x ≤ 0

The area bounded by x-axis = Area of ​​region APO + Area of ​​region OBQ

`= |int_(-1)^0 - x^2 dx| + int_0^1 x^2 dx`

`= |[-x^3/3]|_-1^0 + [x^3/3]_0^1`

`= |-0 - 1/3| + [1/3 - 0]`

`= 1/3 + 1/3`

`= 2/3` square unit