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

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Answer 1 · 2016-03-23T17:13:32

It is # (4(sqrt2-1))/pi#

#1/(b-a) int_a^b f(x) dx#

So the value we seek is

#1/(pi/4-0) int_0^(pi/4) secxtanx dx#

# = 4/pi [secx]_0^(pi/4)#

# = 4/pi [sec(pi/4)-sec(0)]#

# = 4/pi [sqrt2-1]#

# = (4(sqrt2-1))/pi#