# What is the average value of a function f(x) = 2x sec2 x on the interval [0, pi/4]?

Aug 19, 2017

There isn't one

#### Explanation:

Recall that $\sec x$ has a vertical asymptote at $x = \frac{\pi}{2}$.

Thus, $2 x \sec \left(2 x\right)$ has a vertical asymptote at $x = \frac{\pi}{4}$ and there will be no average value for the function on the requested interval.

Attempting to find the average value using an integral:

$\frac{1}{\pi / 4 - 0} {\int}_{0}^{\pi / 4} 2 x \sec \left(2 x\right) \mathrm{dx}$

is impossible because the integral diverges.