Question

Find the area of the region that is enclosed by the graphs of the functions y = x and y = x³.

Answer 1

1/2 square unit

Explanation:

You want the area between the curves y = x³ and y = x.

Area

The area is found by integrating the difference of the function values. It is symmetrical about the origin, so we only need to consider half the figure:

`\displaystyle A=2\int_0^1{(x-x^3)}\,dx=2\left((1^2)/(2)-(1^4)/(4)\right)=\boxed{(1)/(2)}`

The area between the curves is 1/2 square unit.

<95141404393>