Find the area or the region bounded by the curves y = x3 and y = x.

Question

Find the area or the region bounded by the curves y = x³ and y = x.

0.25 

0.5 

1 

2

Answer 1

determine intersection of y=x^3 and y=x

x^3=x means x=0 or x=1

For x between 0 and 1 x^3<x so x lies above x^3 in the x-y plane

To find the area, find ∫ x- x^3 dx with the integral bounds of x=0 and x=1.

Let me know if this helps!