What is the average value of a function #y=secx tanx# on the interval #[0,pi/3]#?

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Answer 1 · 2016-06-05T20:14:45

#3/pi#

The average value of the function #f(x)# on the interval #[a,b]# is equal to

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

Thus, here, the average value is

#1/(pi/3-0)int_0^(pi/3)secxtanxdx#

Note that #d/dx(secx)=secxtanx#, so #intsecxtanxdx=secx+C#.

#=1/(pi/3)[secx]_0^(pi/3)=3/pi(sec(pi/3)-sec(0))=3/pi(2-1)=3/pi#