Finding mean values of a function

[rdajunior95]

The question is :- Find the mean value of (cos 2x)⁷ with respect to x over the interval 0 ≤ x ≤ 0.25(pi), leaving your answer in terms of (pi).


I just don't know the formula for calculating this so if anyone call tell me that hopefully I will be able to solve this question by myself :)

 

[Mark44]

The question is :- Find the mean value of (cos 2x)⁷ with respect to x over the interval 0 ≤ x ≤ 0.25(pi), leaving your answer in terms of (pi).


I just don't know the formula for calculating this so if anyone call tell me that hopefully I will be able to solve this question by myself :)

The mean value of a function f over an interval [a, b] is defined as
$$\frac{1}{b - a}\int_a^b f(x) dx$$

Since there's an integral involved, this should probably have been posted to the Calculus & Beyond section.

 

[rdajunior95]

Thanks, I will try it out and see if I get the answer :)