14.9. Area Under a Curve http://www.ck12.org
It appears that approximations that are 2 units wide produce an area with significant error.
Example C
Logan travels by bike at 20 mph for 3 hours. Then she gets in a car and drives 60 mph for 2 hours. Sketch both the
distance vs. time graph and the rate vs. time graph. Use an area under the curve argument to connect the two graphs.
Solution:Distance vs. Time:
Rate vs. Time:
The slope of the first graph is 20 from 0 to 3 and then 60 from 3 to 5. The second graph is a graph of the slopes from
the first graph. If you calculate the area of the second graph at the key points 0, 1, 2, 3, 4 and 5 you will see that they
align perfectly with the points on the first graph.
TABLE14.14:
x Area under curve from 0 tox
0 0
1 20
2 40
3 60
4 120
5 180