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

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To find the net area between ( f(x) = \cos^2(x)\sin(x) ) and the x-axis over ( x ) in ( [0, 3\pi] ), you need to integrate ( f(x) ) from ( x = 0 ) to ( x = 3\pi ) and then take the absolute value of the result. This is because the function ( f(x) ) dips below the x-axis within the interval, which would otherwise result in negative area. So:

[ \text{Net area} = \left| \int_{0}^{3\pi} \cos^2(x)\sin(x) , dx \right| ]

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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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