Question

Find the average value of the funtion fx=sec^2x on the interval [0,pi/4]

Answer 1

Average value:

`(1)/( ( \pi )/(4) -0) * \int\limits^a_b { sec^(2)x } \, dx`
a = π / 4 , b = 0
= 4/π · tan x = 4/π · ( tan π/4 - tan 0 ) = 4/π · ( 1 - 0 ) = 4/π