Question

The area enclosed by the parabolas x = y² - 1 and x = 1 - y² is ______.

Options

• `1/3`

• `2/3`

• `4/3`

• `8/3`

Answer 1

The area enclosed by the parabolas x = y² - 1 and x = 1 - y² is `underline(8/3)`.

Explanation:

Required area = 4(area of the region OABO)

`=4int_0^1(1-y^2)dy`

`=4[y-y^3/3]_0^1`

`=8/3`