Calc I - Finding average velocity using integration

[opticaltempest]

Can I use integration to show why car 2 traveled farther than car 1 over a given time interval?

Here is some of the problem,

I have the following graph of two different velocity functions
for two cars.

http://img97.imageshack.us/img97/5696/graph1kv.jpg"

The viewing window of this graph is x from 0 to 30
and y from 0 to 100.

After integrating the velocity function I found the position function.
Estimating the distances traveled by both cars from time t = 0
to time = 30 I find,

Car 1 whose velocity function is the thin line on the graph
traveled approximately 964.11 feet.

Car 2 whose velocity function is the thick line on the graph
traveled approximately 1977.9 feet.

By looking at the graph it is obvious that the thick line has
a larger region under the curve (from the curve to the x-axis) than
the thin line.

Is it possible to integrate from 0 to 30 on each velocity function and show that the larger regions under the curve correspond to a higher average velocity over time interval 0 to 30 which is why car 2 traveled farther? Am I on the right track about dealing with the velocities of the cars? Should I also consider their acceleration as being a reason for why car 2 traveled farther?

I need explain why car 2 traveled farther. Is it possible to use integration to find average velocity?

In the original problem velocity is given every 5 seconds from 0 to 30 for each car. I could find the secant line over each 5 second interval and average those secant lines to find the approximate average velocity from time 0 to 30, correct? If possible I want to try to use integration to solve this.

Thanks

 

[Jameson]

You have two velocity graphs and you want to find the average velocity. Your instincts are correct to integrate, but it's not just integrating from 1 to 30. Calculating the average value of a function, f(x), from a to b can be done as follows:

$$A(x)=\frac{1}{b-a}\int_{a}}^{b}f(x)dx$$