Average value function

Question

F(x)=sec^2(x) on interval [0, pi/3]
im getting o please help

Answer 1

1/(b-a) * integral ( f(x)) on (a,b)

 

1/(pi/3 - 0) * integral ( sec^2(x))   on [0,pi/3]

 

3/pi * integral ( sec^2(x)) on [0,pi/3]

 

3/pi * tan(x) on [0,pi/3]

 

3/pi *  [   tan(pi/3 - tan(0) ]

 

3/pi *  [  square-root(3) - 0 ]

 

3*square-root(3)/pi