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

Answer 1

#0#

This is expressed as:

#A=int_0^(3pi)cos(x)dx#
The antiderivative of #cos(x)# is #sin(x)#:
#A=[sin(x)]_0^(3pi)=sin(3pi)-sin(0)=sin(pi)-sin(0)=0#
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Answer 2

To find the net area between ( f(x) = \cos(x) ) and the x-axis over ( x ) in ( [0, 3\pi] ), we integrate ( f(x) ) over the given interval and take the absolute value of the result. The integral of ( \cos(x) ) over ( [0, 3\pi] ) is ( \int_{0}^{3\pi} \cos(x) , dx ). Then, we take the absolute value of this integral to get the net area.

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Answer from HIX Tutor

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.

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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