Question

Find the average value of function
f(t)= 4sec(t)tan(t), interval [0,pi/4]

Answer 1

I assume you have no trouble with the definition of the average value, easily found by using
a) your textbook
b) google

Just integrate over the interval, then divide by the interval length. So, how do we integrate?

Recall that d/dx (sec x) = sec x * tan x

Look familiar?

So, our integral is 4 tan(t) from 0:pi/4

tan(0) = 0
tan(pi/4) = 1

Answer: 1/(pi/4 - 0) * 4(1 - 0)
= 4/pi * 4 = 16/pi