Two cars driven by person A and B start side by side at the beginning of a race. Velocities of the two cars during the race are given below (velocities "v" are in mph and times "t" are in seconds:
Person A
time t : 0 1 2 3 4 5 6 7 8 9 10
velocity 0 20 35 48 62 75 85 93 99 106 111

Person B
time t: 0 1 2 3 4 5 6 7 8 9 10
velocity:0 18 31 43 58 68 79 86 93 95 96

How do I approximate the area between the curves y=vA(t) and y=vB(t) from t=0 to 10, using 10 trapezoids? also what definite integral are we approximating? any help is appreciated!

Question

Two cars driven by person A and B start side by side at the beginning of a race. Velocities of the two cars during the race are given below (velocities "v" are in mph and times "t" are in seconds:
Person A
time t  : 0  1    2    3    4    5    6    7    8    9     10
velocity 0  20  35  48  62  75  85  93  99  106  111

Person B
time t:   0  1    2    3    4    5    6    7    8    9    10
velocity:0  18  31  43  58  68  79  86  93  95   96

How do I approximate the area between the curves y=vA(t) and y=vB(t) from t=0 to 10, using 10 trapezoids? also what definite integral are we approximating? any help is appreciated!

mathmale · Answer

I'd suggest you create a third table obtained by subtracting the data for Person B from the data for Person A.  Then use the resulting velocity differences as the function values, and find the area (which will represent the distance Person A is ahead of Person B) according to the Trapezoidal Rule.

to help you get started:

New table

time   0        1           2
vel      0    20-18   35-31

or

time    0         1           2           3
vel.      0         2           4                 and so on.

anonymous · Answer

Awesome, thank you!