What is the average value of a function f ( x ) = 2 x sec &#x2061;<!-- ⁡ --> 2

skynugurq7

skynugurq7

Answered question

2022-07-04

What is the average value of a function f ( x ) = 2 x sec 2 x on the interval [ 0 , π 4 ]?

Answer & Explanation

zlepljalz2

zlepljalz2

Beginner2022-07-05Added 22 answers

Recall that sec x has a vertical asymptote at x = π 2
Thus, 2 x sec ( 2 x ) has a vertical asymptote at x = π 4 and there will be no average value for the function on the requested interval.
Attempting to find the average value using an integral:
1 π / 4 0 0 π / 4 2 x sec ( 2 x ) d x
is impossible because the integral diverges.

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