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

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- Dec 8th 2006, 05:18 AMgracyplz 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

- Dec 8th 2006, 06:25 AMearboth
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