What is the average value of a function y = sec &#x2061;<!-- ⁡ --> x tan &#x2061;<!--

Extrakt04

Extrakt04

Answered question

2022-06-17

What is the average value of a function y = sec x tan x on the interval [ 0 , π 3 ]?

Answer & Explanation

luisjoseblash2

luisjoseblash2

Beginner2022-06-18Added 16 answers

The average value of the function f(x) on the interval [a,b] is equal to
1 b a a b f ( x ) d x
Thus, here, the average value is
1 π 3 0 0 π 3 sec x tan x d x
Note that d d x ( sec x ) = sec x tan x , s o sec x tan x d x = sec x + C
= 1 π 3 [ sec x ] 0 π 3 = 3 π ( sec ( π 3 ) sec ( 0 ) ) = 3 π ( 2 1 ) = 3 π

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