Calculus Question

Question

A car starts moving at time t=0 and goes faster and faster. Its velocity is shown in the following table.

t (seconds)	0	4	8	12	16
Velocity (ft/sec)	0	8	24	44	74

A. Estimate how far the car traveled during the first 16 seconds using the left-hand sums with 4 subdivisions. Answer: 

__feet 

B. Now estimate how far the car traveled during the first 16 seconds using the right-hand sums with four subdivisions. Answer: 

 __feet 

Determine which of the two is underestimate:

 (choose A or B) 

Answer 1

right side rectangles sum to 600 = 4(8+24+44+74) = 4(150)

left sides to 304 = 4(0+8+24+44) = 4(76)

left is the underestimate

right an overestimate

average is closer: 600+304)/2 = 452 feet