# What is the net area between #f(x)=(x-3)e^x# in #x in[1,2] # and the x-axis?

Area should always be positive.

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To find the net area between the curve ( f(x) = (x-3)e^x ) and the x-axis in the interval ([1,2]), you need to integrate the absolute value of the function over that interval. The net area will be the integral of ( |f(x)| ) from ( x = 1 ) to ( x = 2 ).

[ \text{Net Area} = \int_{1}^{2} |(x-3)e^x| , dx ]

Now, solve this integral to find the net area.

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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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