# What is the net area between #f(x)=ln(x+1)# in #x in[1,2] # and the x-axis?

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To find the net area between ( f(x) = \ln(x + 1) ) and the x-axis over the interval ([1, 2]), you integrate the absolute value of ( f(x) ) over the interval and subtract the integral of the x-axis over the same interval.

The integral of ( f(x) = \ln(x + 1) ) from 1 to 2 is:

[ \int_{1}^{2} \ln(x + 1) , dx ]

The integral of the x-axis (y = 0) over the same interval is simply the integral of 0, which evaluates to 0.

So, the net area is:

[ \int_{1}^{2} |\ln(x + 1)| , 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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