Question

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

Answer 1

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