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:
$\displaystyle l(x)=x$ and
$\displaystyle f(x)=x^3$
The enclosed area is calculated by the difference of these two functions:
$\displaystyle u(x)=l(x)-f(x)=x-x^3$
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:
$\displaystyle A=2\cdot \int_{0}^{1}\left(x-x^3 \right)dx$
I've got A=0.5
I've attached a sketch of the enclosed area.
EB