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The speed of a runner increased steadily during the first three seconds of a race. Her speed at half-second intervals is given in the table.

The speed of a runner increased steadily during the first three seconds of a race. Her speed at half-second intervals is given in the table. Find lower and upper estimates for the distance that she traveled during these three seconds.

t(s) 0 0.5 1.0 1.5 2.0 2.5 3.0

v(ft/s) 0 6.7 9.2 15.5 17.5 19.4 20.2

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