Question

f(t)= -2te^-t^2, [0,5] Find average value.
Attempt: I know that the average value is the integration of f(t) from a to b divided by b-a. I used u substitution to get u= -t^2 and du= -2xdx. I
changed the limits of integration to [0,25] and I got integral of e^u du.
I am not sure if this is right, but then would the integral of that be
just e^u and I would just plug in 25, because I did that and the answer
was wrong.

Answer 1

I don't see anything wrong with your approach. Perhaps there was an arithmetic error lurking somewhere.
What did you get for the answer?
Did you divide the integral by 5 or 25?

Answer 2

You are almost right but since u=-t^(2) the limits are [0,-25] then put them into e^(u) and you get,

e^(-25)-e^(0)=
e^(-25)-1

Then divide that answer by 5 thus the answer is,

(e^(-25)-1)/5