# What is the net area between #f(x) = e^(3-2x)-2x+1# and the x-axis over #x in [0, 3 ]#?

The area of f(x) bounded by

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The sketch of our function is

To find the point at which the curve intersects the axis of theX-axis

the area equal

The area of f(x) bounded by

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To find the net area between ( f(x) = e^{3-2x} - 2x + 1 ) and the x-axis over ( x ) in ([0, 3]), you need to integrate the absolute value of the function within the given interval. Then, you can evaluate the integral. The net area can be expressed as:

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

Substitute ( f(x) = e^{3-2x} - 2x + 1 ) into the integral, take the absolute value, and then integrate over the interval ([0, 3]). After calculating the integral, you will get the net area between the function and the x-axis over the specified interval.

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