Question: Does the definite integral ,also displayed as, always calculate the area bounded by the function f(x) and the x-axis over an interval [a,b]? Why or

  1. Does the definite integral ,also displayed as, 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 thetotal areaof the region bounded by the curve f(x) = x2 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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