# What is the net area between #f(x) = x-sin^2x # and the x-axis over #x in [0, 3pi ]#?

The area is

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To find the net area between ( f(x) = x - \sin^2(x) ) and the x-axis over ( x ) in ( [0, 3\pi] ), you integrate the absolute value of ( f(x) ) from ( x = 0 ) to ( x = 3\pi ). This accounts for both positive and negative regions of the curve. Therefore, the net area is the integral of ( |x - \sin^2(x)| ) from ( 0 ) to ( 3\pi ).

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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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