# How do you find the area between #f(x)=3(x^3-x)# and #g(x)=0#?

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Always draw a graph or sketch when finding an area so that you get an understanding of for the area in question:

graph{ 3(x^3-x) [-2, 2, -3, 3]}

We can easily show that f(x) is an odd function:

If however we wanted the positive contribution area only, then this would be given by:

You should interpret these result depending upon the nature of the initial question!

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To find the area between ( f(x) = 3(x^3 - x) ) and ( g(x) = 0 ), you need to find the definite integral of ( f(x) ) from the points where it intersects the x-axis.

First, find the points where ( f(x) ) intersects the x-axis by setting ( f(x) = 0 ) and solving for ( x ). Then, calculate the definite integral of ( f(x) ) from the smallest x-intercept to the largest x-intercept.

The area between ( f(x) ) and ( g(x) ) is equal to the absolute value of the integral result.

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