Question: 1. Does the definite integral f (x) dr , also displayed as S f (x) dx , always calculate the area bounded by the function

1. Does the definite integral f (x) dr , also displayed as S" f (x) dx , always calculate the area bounded by the function f(x) and the x-axis over an interval [a,b]? Why or why not? 2. How would you calculate the total area of the region bounded by the curve f(x) = x - 2x and the x-axis over the interval [0, 4]? Provide a sketch of this region and work details in calculating the area

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