Maybe I am just bugging out, but I need a sanity check
If $\int_0^4 f(x)dx = C$, what is the average value of $f(x)$?
The question does not include a body for $f(x)$ or a table of values/graph for the output of f(x), so can this question be answered?
I know that: $$\int_a^b f(x)\,dx = F(b)-F(a),$$ will evaluate the integral across a given interval, but the question is asking what the average value of f(x) is, not its integral.
If I take the derivative of the above integral, I can get the function itself, but what do I need to do about the interval $[0, 4]$?
If I take the derivative of the integral, will I be left with $f(x) = 0$ (since the constant will disappear).
Am I thinking too hard about this?
Thanks for the help.