Average Velocity, from t = 1 to t = 5, if velocity in m/s is given by v(t)2tlnt

[on3winyoureyes]

The velocity of an object in m/s is given by v(t)2tlnt. What is the average velocity from t=1 and t=5 seconds?

I know we're supposed to set it up as an integral from 1 to 5. I'm not sure if we need to multiply 1/5 to the integral or not. I think the answer is either 7.059 m/s or 28.236 m/s

 

[Ishuda]

The velocity of an object in m/s is given by v(t)2tlnt. What is the average velocity from t=1 and t=5 seconds?

I know we're supposed to set it up as an integral from 1 to 5. I'm not sure if we need to multiply 1/5 to the integral or not. I think the answer is either 7.059 m/s or 28.236 m/s

One of the ways to remember this is that the average of some function F(x) over an interval (a,b) is a constant A so that the integral over the interval (a,b) of both A and F(x) are the same. That is
\(\displaystyle \int_a^b\, F(x)\, dx\, =\, \int_a^b\, A dx\, =\, Ax|_a^b\, =\, A\, (b-a)\)
or
\(\displaystyle A\, =\, \frac{1}{b-a}\, \int_a^b\, F(x)\, dx\)