Question

The area enclosed between the curves y = x^2, and y = `sqrtx` is, (in square units) ______ 

Options

• `1/3`

• `5/4`

• `5/12`

• `12/5`

Answer 1

The area enclosed between the curves y = x^2, and y = `sqrtx` is, (in square units) `underline(1/3)`. 

Explanation:

Given curves are y = x² and y = `sqrtx`

On solving, we get x = 0, x = 1

∴ Required area = `int_0^1 (sqrtx - x^2)dx`

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

= `2/3 - 1/3 = 1/3`