# Math Help - plz help area between curves

1. ## plz help area between curves

1>find the area bounded by the graph of y=x and y=x^3.Providesketch of the region on axis

2. Originally Posted by gracy
1>find the area bounded by the graph of y=x and y=x^3.Providesketch of the region on axis
Hello, Gracy,

you have the graphs of 2 functions:
$l(x)=x$ and
$f(x)=x^3$

The enclosed area is calculated by the difference of these two functions:
$u(x)=l(x)-f(x)=x-x^3$

Calculate the zeros of u. These zeros correspond with the intercepts of l and f. You'll get: x = -1 or x = 0 or x = 1

For symmetry reasons the area can be calculated as:

$A=2\cdot \int_{0}^{1}\left(x-x^3 \right)dx$

I've got A=0.5

I've attached a sketch of the enclosed area.

EB