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This problem offers three different ways to take a Riemann Sum. Because the function is increasing, a left approximation will be an underestimate and a right approximation will be an overestimate. In most cases, a trapezoidal sum is the most accurate method out of these three methods.
The left approximation is calculated by splitting up the total interval of the velocity graph from 0 to 5 seconds into the given 4 sub-intervals, and the area of each sub-interval is calculated and shown above. If the segment is pictured as a bar on a graph, the "width" of the rectangle would be the length in seconds of the interval and the "height" of the rectangle would be the velocity that corresponds to the smaller time value.
The right approximation is calculated by splitting up the total interval of the velocity graph from 0 to 5 seconds into the given 4 sub-intervals, and the area of each sub-interval is calculated and shown above. If the segment is pictured as a bar on a graph, the "width" of the rectangle would be the length in seconds of the interval and the "height" of the rectangle would be the velocity that corresponds to the larger time value.
The trapezoidal approximation is calculated by splitting up the total interval of the velocity graph from 0 to 5 seconds into the given 4 sub-intervals, and the area of each sub-interval is calculated and shown above. If the segment is pictured as a bar on a graph, the "width" of the rectangle would be the length in seconds of the interval and the "height" of the rectangle would be the average of the velocities that correspond to the smaller and larger times.
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