Question

The area enclosed between the parabola y² = 4x and line y = 2x is ______.

Options

• `(2)/(3)` sq units

• `(1)/(3)` sq unit

• `(1)/(4)` sq unit

• `(3)/(4)` sq unit

Answer 1

The area enclosed between the parabola y² = 4x and line y = 2x is `bbunderline((1)/(3) "sq unit")`.

Explanation:

Area = `int_0^1 [2sqrt x - 2x]`

= `2[(x^(3//2))/(3/2) - x^2/2]_0^1`

= `2(2/3 - 1/2) xx 1`

= `4/3 - 1`

`1/3` sq. units.