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 below. Find lower and upper estimates of the distance she covered during the first three seconds of the race. Use left- and right- rectangles. Do not use midpoint rectangles. In order to get the best estimates, use 0.5 rectangle widths.

Question

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 below. Find lower and upper estimates of the distance she covered during the first three seconds of the race. Use left- and right- rectangles. Do not use midpoint rectangles. In order to get the best estimates, use 0.5 rectangle widths.
 Enter your answer as a Riemann sum to show your work.

The lower estimate is:
The upper estimate is:

t(sec)   0 0.5  1   1.5   2   2.5   3
v(ft/sec)0 6.8 12.4 16.4 19.5  23  23.8