# What is the net area between #f(x) = cos2x-xsinx # and the x-axis over #x in [0, 3pi ]#?

The net area between

Using the DI method (an easier way to understand integration by parts):

Multiply the diagonals with the appropriate sign, and add them (and don't forget the negative sign in front of the integral from before):

That is the net area under the curve. Hope this helped!

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To find the net area between ( f(x) = \cos(2x) - x\sin(x) ) and the x-axis over ( x ) in ( [0, 3\pi] ), we need to compute the definite integral of the absolute value of ( f(x) ) over the given interval.

( \text{Net Area} = \int_{0}^{3\pi} |f(x)| , dx )

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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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