# What is the net area between #f(x)=x^3+4x^2-2# in #x in[2,5] # and the x-axis?

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To find the net area between the function ( f(x) = x^3 + 4x^2 - 2 ) and the x-axis in the interval ([2,5]), you need to integrate the absolute value of the function from ( x = 2 ) to ( x = 5 ). Mathematically, this is represented as:

[ \text{Net Area} = \int_{2}^{5} |f(x)| , dx ]

First, determine the intervals where the function is above and below the x-axis in the interval ([2,5]). Then integrate the function over those intervals, taking the absolute value to ensure a positive area.

[ \text{Net Area} = \int_{2}^{3} (x^3 + 4x^2 - 2) , dx + \int_{3}^{5} -(x^3 + 4x^2 - 2) , dx ]

Calculate each integral separately and add their absolute values to find the net area.

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