Hey achui17.
Can you show us your working out for this problem?
A wheel has angular position theta = 0 (radians) at t = 0 (seconds). It then rotates with an angular velocity equal to .72t radians/sec. In radians per second, what is the average angular velocity from theta = 4 radians to theta = 9 radians? I got 3 for my answer but I'm not sure if it's right
That looks pretty good.
Finding the average velocity is simply integrating the velocity over a particular region and then dividing by the length of that region (region in this case is time).
Since the anti-derivative of velocity is just displacement (or position), then the integral will be P(5) - P(10/3) and the average just dividing this by (5 - 10/3) which is what you have done.
R confirms your results as well:
> 4/0.36
[1] 11.11111
> 100/9
[1] 11.11111
> 9/0.36
[1] 25